Page 1
Dr. Veena Mathad M.Sc ,Ph.D
Designation : Assistant Professor
Email id : [email protected]
Phone Number : 9741770483
Area of Specialization : Graph Theory
Research Area : Graph Theory – Graph Operators, Graph Equations, Algorithms, Fuzzy
graphs, Domination Parameters, Signed Graphs.
Number of Publications : 16
List of Publications :
1. The mass graph and the total-mass graph of a graph, Acta Ciencia Indica, Vol.XXXM
(2004), No.3, pp.635-643 (with B.Basavanagoud).
2. On Pathos Plick graph of a tree, Proceedings of the National Conference on GAMCA, 9-11
Dec 2004, Kuvempu University, Shankaraghatta, Shimoga (with B.Basavanagoud).
3. Graph equations for line graphs, blitact graphs and blict graphs, Journal of Discrete
Mathematical Sciences and Cryptography, Vol.8 (2005), No.3, pp.373-379 (with
B.Basavanagoud).
4. Miscellaneous properties of line splitting graphs, Proceedings of the National Conference
on Graphs, Combinatorics, Algorithms and Applications, Narosa Ps. House, NewDelhi
(2005) (with B.Basavanagoud).
5. Graph Equations for line graphs, qlick graphs and Plick graphs, Proceedings of the National
Conference on Graphs, Combinatorics, Algorithms and Applications, Narosa Ps. House,
NewDelhi (2005) (with B.Basavanagoud).
6. Graph equations for line graphs, jump graphs, middle graphs, litact graphs and lict
graphs, Acta Ciencia Indica, Vol.XXXIM (2005), No.3, pp.735-740 (with B.Basavanagoud).
7. Graph equations for line graphs, litact graphs and lict graphs, International Journal of
Management and Systems, Vol.22 (2006), No.2, pp.103-110 (B.Basavanagoud and C.
Sulochana).
8. Characterizations of minimally nonplanar mass graphs, Journal of Analysis and
Computation, Vol.2 (2006), No.1, pp.23-31 (with B.Basavanagoud).
9. On pathos qlick graph of a tree, Proceedings of the National Academy of Sciences, India
sect. A, Vol.78, Pt. III, (2008) (with B.Basavanagoud).
10. Traversability, Covering Invariants, k-Trees of Line Splitting Graph of a Graph,
Proceedings of the International Conference on Graph Theory and its applications,
Macmillon Publishers India Ltd., New Delhi (2009) (with B.Basavanagoud).
11. An Algorithm to determine the chromatic number of a graph, International Journal of
Physical Sciences, Ultra Scientist Vol.21(2)M, 577-579(2009) (with Shantharaju C.V.)
12. By Adjacency Matrix An Algorithm to determine the chromatic number of a graph" (accepted) International Journal of Physical Sciences, Ultra Scientist Vol 22(1) April 2010.
13. Connectivity of Smarandachely Line Splitting Graphs, B.Basavanagoud and Veena Mathad,
International J.Math. Combin. Vol.4 (2010), 08-12
14. Graph Equations for Line Graphs, Jump Graphs, Middle Graphs, Splitting Graphs and Line
Splitting Graphs, B.Basavanagoud and Veena Mathad, Mapana J Sci, Vol. 9, No.2, July-
December 2010
15. Graph equations for line graphs, middle graphs, semi-splitting block graphs and semi-line
splitting block graphs, Veena Mathad, Proceedings of the Jangjeon Mathematical Society, 14
(2011) No. 2, pp.209-214.
16. Neighborhood Connected Neighborhood Number of Graphs, Veena Mathad, International
Journal of Mathematics Research, Vol.4, No.2 (2012), pp.193-199.
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Dr. Soner Nandappa D. M.Sc.,M.Phil.,Ph.D
Designation : Professor of Mathematics
Email id : [email protected]
Phone Number : 9945779695
Area of Specialization : Graph Theory
Research Area :Domination Theory and its related topics
No of Publications:64
List of Publications :
1. Entire Domination of Graphs, Advanced in Graph theory, ed., V. R. Kulli, Vishwa
International Publications, 1991)237-243(V.R.Kulli).
2. The independent neighborhood number of graphs, Nat. Acad.Sci, letter 19(1996)(with V. R.
Kulli).
3. Efficient bondage number of a graphs, Nat. Acad. Sci, letter19(1996) 997-201(with V. R.
Kulli).
4. Complementary edge domination the Graphs, Indian J. Pure and Applied Mathematics 28(7)
(1997) 917-920(with V. R. Kulli).
5. The Maximal Neighborhood number of a Graph, Far East J.Appl. Math. 5(3)(2001) 301-307
(with B. Janakiram and Chaluvaraju).
6. The Block Number of Graph, Proc. Nat. Conf. On Challenges of the 21st century in Maths
and its allied topics, ed., B. S. Kiranagi, (2001) 296- 301(with V. R. Kulli).
7. The Split Total Domination number of a Graph, Proc. Nat. Conf. On Challenges of the 21st
century in Maths and its allied topics, ed., B. S. Kiranagi, (2001)311-316(with B.
Chaluvaraju).
8. The Efficient Domatic Number of a Graph, Proc. Nat. Conf. On Challenges of the 21st
century in Maths and its allied topics, ed., ed., B. S.Kiranagi, (2001)283-287(with
Puttaswamy).
9. Total Split Domination in Graphs, Far East J. Appl. Math. 6(1)(2002) 89- 95(with B.
Janakiram and Chaluvaraju).
10. Double Edge Domination in Graphs, Proceedings of the Jangjeon Mathematical Society,
South Korea, 5(1)(2002) 15-20(with B. Chaluvaraju).
11. The Block Neighbourhood Number of a Graph, Far East J. Appl. Math., 9(2)(2002) 127-135
(with Puttaswamy).
12. Complimentary Neighbourhood in Graphs, Nat. Acad. Sci Lett., 26(9- 10)(2003) 271-275
(with B. Janakiram and M. A. Davis).
Page 3
13. The Connected Efficient Domination number of a Graph, IJOMS 19(1)(2003) 37-42(with V.
R. Kulli).
14. Domination in 2-Complement (2(i)-Complement) of a Graph, Advanced Studies in
Contemporary Maths. 7(2)(2003) 145-154(with B. Janakiram and B. Chaluvaraju).
15. The Connected Double Domination number of a Graph, Acta. Ciencia Indica,
29M(2003)237-242(with B.Chaluvaraju).
16. Complementory Edge Neighbourhood in Graph, Far East J. Appl. Math. 11(3)(2003)177-
182(with B. Janakiram and M. A. Davis).
17. Uniform Neighbourhood Number of a Graph, Proceedings of the Jangjeon Mathematical
Society, 6(2)(2003) 125-135(with B. Chaluvaraju).
18. Maximal total domination number of a graphs. The Aligarh Bull. Of Maths. 22(1)(2003) 29-
33(with Puttaswamy).
19. The double global domination number of a graph, Journal of Indian Math. Soc. 70(1-4)
(2003) 191-195 (with B. Chaluvaraju and B. Janakiram).
20. Total Nonsplit domination number of a graph, The Maths. Education 38(2)(2004) 77-80(with
B. Chaluvaraju).
21. Maximal edge neighborhood in graphs, Indian Journal of Mathematics 46(2 & 3) (2004) 283-
291, (with B. Janakiram and B. Chaluvaraju).
22. Global neighbouhood in graph, Acharya Nagarjuna Int. J. of Maths. And Inf. Tech.
1(2004)01-11(with Puttaswamy).
23. Complementary acyclic domination in graphs, Journal of the Indian Math. Soc. 71(1-
4)(2004) 221-226(with Janakiram and M. A. Davis).
24. The paired neighbouhood number of a graph, Proc. Of the Jangjeon Mathematical soc.
8(1)(2005) 113-121(with B. Chaluvaraju).
25. Vertex-set neighbourhood and strong nonsplit neighbourhood parameters in graphs, Ultra
Science 17(1) (2005) 35-40(with Puttaswamy).
26. Paired neighbourhood in graphs, Far East J. Appl. Math. 22(2)(2006) 215- 224(with B.
Chaluvaraju and K. M. Yogeesha).
27. The connected total domination number of a graph, Journal of Analysis and computation,
2(2)(2006) 183-189(with V. R. Kulli).
28. Neighbourhood in subdivision graphs, Ultra Science 18(2)M,(2006)243- 248(with
Puttaswamy).
29. The k-nonsplit domination number of a graph, IJOMS, 22(1)(2006)53-58. (with B. Janakiram
and B. Chaluvaraju).
30. H-adjacent domination in graphs, Nat. Acad. Sci Lett. 29(7,8)(2006) 293- 297(with B.
Janakiram and M. A. Davis).
Page 4
31. Vertex Component domination in graphs, Indian Journal of Mathematics, 48(1)(2006) 57-
62(with B. Janakiram and M. A. Davis).
32. The double bondage number of a graph, Ultra Science, 19(2)M(2007) 439- 442(with K. M.
Yogeesh).
33. Complementary total domination in graphs, Journal of Discrete Mathematical Science and
Cryptography, 10(4)(2007)505-516(with B. Chaluvaraju).
34. Fuzzy Covering and Fuzzy Neighbourhood set in Fuzzy Graphs, Ultra Science 19(3)M(2007)
601-608(with Q. M. Mahioub).
35. The nonsplit domination number of Fuzzy graphs, Bull. Pure Appl. Math. 1(2)(2007) 200-
207(with Q. M. Mahioub).
36. The Double domination number of fuzzy graphs Journal of Applied Mathematical Analysis
and Applications, 3(2) (2007) 97-104(with Q. M.Mahioub).
37. On the number of minimum independent dominating sets in paths and cycles, Journal of
Applied Mathematical Analysis and Applications, 3(2)(2007) 155-169(with K. M. Yogeesh).
38. Disjoint perfect domination number of a graph, Journal of Applied Mathematical Analysis
and Applications, 3(2)(2007) 171-179(with B. Sharada).
39. On independent neighbourhood and Coloring graphs, Advances in Theoretical and applied
Mathematics, 2(2007) 117-122(with S. Ghobadi).
40. Partially balanced incomplete block designs arising from minimum efficient dominating sets
of a graphs, Bull. Pure Appl. Math. 2(1)(2008) 47-56(with B. Sharada).
41. Inverse dominating set in Fuzzy graphs Proce. Of the Jangjeon Mathematical Society,
11(1)(2008) 75-81(with S. Ghobadi and Q. M. Mahioub).
42. Nomatically Cocritical Graphs, Ultra Science 20(1)M(2008) 205-208(with S. Ghobadi and K.
M. Yogeesha).
43. The Split domination number of fuzzy graphs, Far East Journal of Appl. Maths 30(1)(2008)
125-132(with Q. M. Mahioub).
44. The Split edge domination number of a graph, Far East J. of Appl. Maths. 30(1)(2008) 93-
100.(with K. M. Yogeesha and S. Ghobadi).
45. The Nomatic number problem in interval graphs, Far East J. of Appl. Maths, 30(2)(2008)235-
244(with S. Ghobadi).
46. Roman edge domination in graphs,Proc. Nat. Acad. Sci. Lett. (79)(2009) 45-50,(with B.
Chaluvaraju and J. P. Srivastava).
46. Swithing equivalence in symmetric n-Sigraphs-II,J. Orissa Math. Soc. 27(2)(2009)-(to
nappear)(with R. Rangarajan and P. Siva Kota Reddy).
47. The block perfect domination number of a graph,Advances and applications in Discrete
Mathematics 4(2), (2009), 161-168,(with S. R. Ramachandra).
Page 5
48. Connected neighborhood number in a Fuzzy graphs,ACM Journal (2009)(with A. Arunkumar
and Q. M. Mahioub).
49. The Perfect domatic number of factors of graphs, international Journal of physical
sciences,22(3),M(2010),862-866.
50. Roman k-edge domination in graphs, Ultra scientists of physical science, 22(3m)(2010) 203-
207, (with S. R. Ramachandra).
51. Design associated with maximum independent set of Cubic Graphs, Journal of Computer and
Mathematical sciences 1(3), (2010), 300-309.(with P.N.Vinay kumar).
52. Strong Domination critical and stability in graphs, J. Comp. and math. Sci. 1(3) 2010, 294-299,
(with S. R. Ramachandra).
53. Mth power symmetric n-sigraphs, Italian Journal of pure and Applied Mathematics (2011)(To
appear) )(with R. Rangarajan and P. Siva Kota Reddy).
54. Total numbers of special kinds of neighbourhood sets of graphs, international journal of
Mathematical Archive 2(4), (2011),433-437( with M. P Sumathi).
55. Partial Balanced incomplete Block Designs Arising from a Maximal independent set of an
SRNT Graph, Advanced and Applications in Discrete Mathematics 7(2)(2011), 121-128 (with
A. Alwardi and G. Deepak)
56. On the common neighbourhood domination number, Journal of Computer and Mathematical
sciences 2(3)(2011), 547-556 (with A. Alwardi and K.Ebadi).
57. Some results on swiched graphs, Journal of Computer and Mathematical sciences 2 (2011),
260-264 (with A. Alwardi and M. P.Sumathi).
58. On the number of minimum neighbourhood sets in paths and cycles, General Mathematics
Notes 3(1), 2011(with M.P. Sumathi).
59. Partially balanced incomplete block designs associated with minimum perfect dominating sets
of Clebsch graph, International Journal of Applied Mathematics and Computations.(with
P.N.Vinay kumar).
60. Equi-degree energy of graphs, International Journal of computational science and
Mathematics.(with P.N.Vinay kumar).
61. The Maximal equitable domination number of a graph, Journal of Computer and Mathematical
sciences, Vol.2 (4), 617-620 (2011) .(with P.N.Vinay kumar).
62. On the common–neighborhood energy of a graph, Bulletin de l'Acad_emie Serbe des Sciences
et des Arts (Classe des Sciences Math_ematiques et Naturelles) (36) (2011) 49-59 (with A.
Alwardi and Ivan.Gutman).
63. Some Induced Subgraphs of StronglyRegular Graphs with no Triangles, International
Mathematical Forum, Vol. 6, 2011, no. 46, 2261 – 2266 (with A. Alwardi).
64. Association scheme on some Cycles, my SCIENCE, (with M.P. Sumathi).
Page 6
Books Published:
1 Discrete Mathematics,
No. of Ph. D's guided - awarded : 9
No. of Ph. D's guided - in progress : 6
Page 7
Dr. Chandrashekar Adiga M.Sc ,Ph.D Designation : Professor of Mathematics
Email id : [email protected] , [email protected]
Phone Number : 9448888276/0821-2419830
Area of Specialization : Special Functions, Number Theory, Partition Theory,
Discrete Mathematics and Graph Theory.
Research Area : Special Functions, Number Theory, Partition Theory, Discrete
Mathematics and Graph Theory.
No of Publications: 93
List of Publications : INTERNATIONAL:
1. simple proof for finite double series representations for the Bernoulli, Euler and Tangent
Numbers., Int.J.Math.Edu.Sci,Technol. (U.K.) vol.14 Nos. 5(1983) 652-654. C.Adiga
(with S.Bhargava)
2. On some Continued fraction identities of Srinivasa Ramanujan, Proc.Amer,Math.Soc.
Vol.92 No.1 (1984) 13-18.C.Adiga (with S.Bhargava).
3. Two generalizations of Ramanujan's continued fraction identities,Lecture Notes in
Mathematics. Springer-Verlag, Vol.1122,(1984) 56-62 C.Adiga (with S.Bhargava).
4. Chapter 16 of Ramanujan's Second Note Book: Theta functions and Q.Series .
Mem.Amer,Math. Soc. Vol.53 Vol.315(1985) 1-85 C.Adiga (with B.C.Berndt, S.Bhargava
& G.N.Watson)
5. On two elliptic θ- function identities stated by Srinivasa Ramanujan
Int.J.Math.Edu.Sci,Technol.(U.K.)Vol.18 No.2 (1987)318-320 C.Adiga (with S.Bhargava)
6. Simple proofs of Jacobi's two and four square theorems. Int.J.Math.Edu.Sci,Technol.
(U.K.) Vol.18 No.2 (1987)318-320 C.Adiga (with S.Bhargava )
7. 7. An estimate of Ramanujan related to the greatest integer function.Bull Austral
Math.Soc.Vol.44.No.1(1991) 149-154. C.Adiga (with S.Bhargava and
D.D.Somashekara).
8. A generalization of Shiokawa's Rational Approximations to Roger's-Ramanujan Continued
Fraction.Commentary Mathematici,Vol.41. No.2(1992) 125-134.C.Adiga (with
S.Bhargava and D.D.Somashekara).
9. On the representations of an integer as a sum of two or four triangular
numbers.Nihonkai Math. Hiyr,Vol.3 No.2 (1992) 125-131 C.Adiga.
10. Ramanujan's 11 Summation and an interesting convolution identity.Bull Austral,
Math.Soc.Vol.47,No.1(1993)155-162C.Adiga (with S.Bhargava and D.D.Somashekara).
Page 8
11. On the representations of an integer as a sum of square and thrice a
square.Int.J.Math.Educ.Sci, Technol.Vol.24,No.3(1993)493-498. C.Adiga (with
S.Bhargava and D.D.Somashekara).
12. Three square theorem as an application on Andrew's identity. Fibonacci Quarterly,
May(1993) 129-133. C.Adiga (with S.Bhargava and D.D.Somashekara).
13. Jacobi's two square and four square theorems via. Roger's identity.Tamkang
Jour.Math.Vol.25.No.1(1994)23-27.C.Adiga.
14. A basic bilateral series summation formula and its applications.Integral Transforms and
Special Functions, Vol.2 No.3 (1994) 165-184C.Adiga (with S.Bhargava ).
15. A note on q-gamma and q-beta functions, Mathematica Balkanica, Vol.9 (1995) 35-
41.C.Adiga .
16. Ramanujan's summation formula and its applications,Proceedings of the International
Conference on Transcedental Number Theory,Tokyo, 3-5 Dec(1996)8-26.C.Adiga.
17. On some Rogers-Ramanujan type continued fraction identities,Mathematica Balkanica,
New Series Vol.12,(1998) Nos. -2,37-45.C.Adiga (with D.D.Somashekara).
18. On some new identities involving integrals of theta-functions,Advanced Studies in
contemporary Mathematics V0l.3 o.2(2001)1-11.C.Adiga (with K.R.Vauki and
M.S.Mahadeva Naika).
19. Some new explicit evaluations of Ramanujan's Cubic Continued fraction,New Zealand
Jour. Math Vol.13(2002),109-114C.Adiga (with K.R.Vauki and M.S.Mahadeva Naika).
20. Ramanujan's remarkable summation formula as a 2-parameter generalization of the
quintuple product identity,Tamkang Jounal ofMathematics, Vol.33,No.3,(2002),285-
288.C.Adiga (with S.Bhargava and M.S.Mahadeva Naika).
21. A new class of modular equation akin to Ramanujan's P-Q eta-function identities and
some evaluations there from,Advanced Studies in contemporary
Mathematics,(Kyungshang)Vol.5,1(2002).no.1,21-34.C.Adiga (with S.Bhargava and
M.S.Mahadeva Naika).
22. On a generalization of Sandor's functions Proc. Jangjeon
Math.Soc.Vol.5,No.2 (2002)121-124 .C.Adiga (with T.Kim).
23. Common fixed points for sequence of mappings, Proc.Jangjeon Math. Soc. Vol.5,
No.1(2002)21-34.C.Adiga (with iniswamy)24. A note on the values of (2k +
1),Advanced studies in contemporary Mathematics, Vol.5, o.2(2002)163-166.C.Adiga
(with L.C.Jang,T.Kim,Y.H.Kim,H.K.Pate and D.W.Park).
24. Some theta function identities and new explicit evaluation of Rogers-Ramanujan
continued fraction, Tamsui Oxfor Jour. ath. Sci. Vol.18 No.1(2002)101-117.C.Adiga
(with K.R.Vauki and K.Shivashankara).
25. Continued fraction representations for theta functions,Proc. Jnagjeon Math. Soc. Vol.5,
No.2(2002),115-120, NNTDM 9(2003),7-12.C.Adiga (with T.Kim,D-W.Parts, Y.S.Ro and
L-C Jang)
Page 9
26. A fixed point theorem on some non expansive type mappings on complete metric spaces.
Fixed Point Theory and Applications Vol.4, (2003) 1-9. C.Adiga (with Giniswamy)
27. On a continued fraction of Ramanujan, Tamsui Oxford Jour. Math. Sci. Vol.19, No.1
(2003) 55-65.C.Adiga (with T.Kim)
28. Modular equations in the theory of signature 3 and P-Q identities, Advanced Studies in
Contemporary Mathematics 7 (2003)No.1, 33-40.C.Adiga (with T.Kim and Mahadeva
Naika). On a q-analogue of Sandor's function .J. Inequal, Pure and Applied
Math.4(4)(2003)1-5 C.Adiga (with T.Kim ,D.D.Somashekara and Syed Noor Fathima ).
29. On some transformation formulas for basic bilateral hypergeometric series, Proc. Of
14th International Conference of the Jangjeon Mathematical Society C.Adiga (with
D.D.Somashekar and Syed Noor Fathima)
30. A note on strongly multiplicative graphs, Discussions mathematicae Graph Theory,
24(2004) 81-83. C.Adiga (with D.D.Somashekar and H.N.Ramaswamy)
31. General relations between sums of squares and sums of triangular numbers, Discrete
Mathematics C.Adiga (with Shaun Cooper and Jung Hun Han).
32. Sums of products of generalized Bernoulli Numbers, Int. J. Math. Vol.5, No.1 (2004) 1-7.
C. Adiga (With T. Kim).
33. On a certain class of add-even partitions, Proc. Jangjeon Math. Soc. 7(2004) No 2, 89 -
94. C. Adiga (with S. Bhargava and A.K.Agarwal)
34. A Note on a Certain Continued fraction of Ramanujan Bull. Austral. Math. Soc. 70
(2004), 489-497.C. Adiga (with N. Anitha).
35. On transformation of basic bilateral series, Proc. Jangjeon Math. Soc, 8 (2005) No 1,
107-112. C. Adiga (with D.D.Somashekara and S,N.Fathima).
36. A new approach to Jacobi's theorems via Ramanujan's continued fractions, Bull.
Austral. Math. Soc. Vol. 71(2005) 75-79. C. Adiga (with Jung Hun Han).
37. A. General relation between sums of squares and sums of triangular numbers, Int. Jour.
Number theory Vol. 1. No. 2 (2005) 175-182.C. Adiga (with Shaun Cooper and Jung Hun
Han).
38. On the q-analogue of Gamma function and related inequalities I. Inequal. Pure and
Applied Math Vol. 6 No 4 (2005) 1-8.C.Adiga (with Taekyun Kim).
39. On some continued fractions of Ramanujan, Adv. Stud. Cont. Math., No.1, 12(2006),
155-162. C.Adiga (with N. Anitha).
40. On a reciprocity of Ramanujan, Tamsui Oxford J. Math. Sci., Vol. 22 No.1, (2006), 9-
15.C.Adiga (with N. Anitha).
41. An upper bound for maximum number of edges in a strongly multiplicative graph,
Discussiones Mathematicae Graph Theory, 26(2006), 1-5. C.Adiga (with M. Smitha).
42. On colorings of strongly multiplicative and strongly quotient graphs, Adv. Stud. Cont.
Math., Vol. 13 No.2, (2006), 171-182. C.Adiga (with R. K. Zaferani).
Page 10
43. More graphs whose energy exceeds the number of vertices, Iranian Journal of
Mathematical Sciences and Informatics, Vol. 2 No.2, (2007), 13-19.C.Adiga (with
Zeynab Khoshbakht and I. Gutman).
44. Upper bounds for energy of a graph, Adv. Stud. Cont. Math., Vol. 16 No.2, (2008), 279-
285.C.Adiga (with R. K. Zaferani).
45. A note on certain divisibility problem, Int. Jour. Math. Analysis, Vol 2 No.24, (2008),
1157-1161.C.Adiga (with H. N. Ramaswamy).
46. Biregular graphs whose energy exceeds the number of vertices, MATCH
Communications in Mathematical and in Computer Chemistry, No. 3, Volume 62(2009)
499-508.C.Adiga (with I. Gutman, Antoaneta Klobucar and Snjezana Majstorovic).
47. 49. On Maximum degree energy of a graph, International Journal of Contemporary
Mathematical Sciences, Vol. 4, 2009, No. 8, 385-396.C.Adiga (with M. Smitha).
48. On strongly sum difference quotient graphs, Advanced Studies in Contemporary
Mathematics, 19 (2009), No. 1, pp. 31-38.C.Adiga (with C. S. S. Swamy).
49. On the Skew Laplacian Energy of a digraph, International Mathematical Forum, 4, 2009,
no. 39, 1907-1914. C.Adiga (with M. Smitha).
50. On the Skew energy of some unitary Cayley digraphs, Adv. Stud. Contemp. Math. 21.
(Accepted for publication). C. Adiga (with H. N. Ramaswamy, D. D. Somashekara and Z.
Khoshbakht).
51. Bounds on the largest of minimum degree eigenvalues of graphs, International Math. Fourm 5, 37-40 ( 2010)1823-1832. C. Adiga(with C. S. Shivakumar
Swamy)
52. The skew-energy of a digraph, Linear Algebra and its applications 432(2010)1825- 1835.
C. Adiga(with R. Balakrishnan and Wasin So).
53. A Note on Skew Energy of a Digraph, Adv. Stud. Contemp. Math. 20 No 1. (2010).
C. Adiga (with T.Kim,Y.H. Kim,J Choi, and B.Lee).
54. Quintuple Product Identity as a Special Case of Ramanujan’s Summation Formula Asian-European Journal of Mathematics, 4, No 1 ( 2011) 31-34. C. Adiga
55. On Edge-balance Index Sets of N cycles Three Nested Graph ( n=0,1,2 ( mod 6), Adv. Stud. Contemp. Math 21 No 1.(2011) 85-93. C. Adiga (with Ying Wang, Yuge Zheng and Shrikanth A S)
56. Bounds on the largest of minimum degree Laplacian eigenvalues of a graph,
International J. math. combin. 2( 2011) 130-136. C. Adiga (with C. S. Shivakumar Swamy)
57. On 1-edge balance index set of some graphs, Proc. Jangjeon Math. Soc. 14(2011) No. 3, 319-331 . C. Adiga (with C K Subbaraya, Shrikanth A S and Shriraj M. A)
Page 11
NATIONAL:
58. A basic hypergeometric transformation of Ramanujan and generalization. Indian J.Pure,
Appl.Maths.Vol.17 No.3 (1986) 338-342.C.Adiga (with S.Bhargava).
59. One some identities in the theory of elliptic functions found in the note books of
Srinivasa Ramanujan. Mysore University Journal vol.No.XXX (1987) 117-125.C.Adiga
(with S.Bhargava).
60. On some generalizations of Ramanujan's continued fraction identities. Proc.Ind. Acad
Sci. Vol.97 (1987) 31-43.C.Adiga (with S.Bhargava and D.D.Somashekara).
61. On certain continued fractions related to 32 Basic Hypergeometric functions,
Jour.Math.Sci,Vol.21, No.6(1987)613-629. C.Adiga (with S.Bhargava and
D.D.Somashekara).
62. Parity results deducible from certain theta function identities found in chapter of
Ramanujan's second note book.Math.Student,Vol.57,Nos 1-4 (1989) 121-132. C.Adiga
(with S.Bhargava and D.D.Somashekara).
63. Some relations between infinite series and infinite products, Proceedings of the
symposium on Algebra and Number theory.Cochin,India, 27-28, July (1990) 23-
29,C.Adiga (with S.Bhargava and D.D.Somashekara).
64. A note on Ward's conjecture. Jour.Ind.Math.Soc.Vol.59,(1993)201-206. C.Adiga(with
N.R.Mohan).
65. A note on Euler's totient function .Jour.Ind.Math.Soc.Vol.62, Nos.1-4 (1996),169-
174).C.Adiga (with H.N.Ramaswamy).
66. Some interesting applications of Ramanujan's identities to representations of integersas
sums of squares. Presented at 62nd Annual Conference of IMS held at IIT Kanpur during
22-25 Dec.1996.C.Adiga (with S.Bhargava and D.D.Somashekara).
67. A note on rational approximations Presented at 62nd Annual Conference of IMS held At
IIT Kanpur during 22-25 Dec.1996. C.Adiga (with D.D.Somashekara and K.R.Vasuki).
68. A note on rational approximations. Jour.Ind.Math.Soc.Vol.65, Nos.1-4(1998),181-
189.C.Adiga (with K.R.Vasuki).
69. Number of representations of an integer as a sum of a square and five times a
square.Jour.Ind.Math.Socl.Vol.65 Nos. 1-4(1998)249-251. C.Adiga (with S.Bhargava and
D.D.Somashekara).
70. Ramanujan's 1 1 summation and an interesting generalization of an identity of Jacobi.
Indian Jour.Math.Socl.Vol.41 Nos.1-4(1999) 39-42. C.Adiga (with S.Bhargava and
D.D.Somashekara).
71. A fixed point theorem in four metric spaces, Jour.Nat and Phy, Sci,Vol.14,Nos. 1-
2(2000)105-110.C.Adiga (with Giniswamy and S.L.Singh).
72. Some explicit evaluations of theta-functions, Far East J,Math. Sci , Vol.2(4)(2000), 625-
631.C.Adiga (with K.R.Vasuki ).
Page 12
73. On Some Continued fraction expansions for ratios of 22 , Special Functions :Selected
Articles, P.K.Banerji(Ed),Scientific Publisher, India, (2000) 1-16, Jodhpur,2001. C.Adiga
(with R.Y.Denis and K.R.Vasuki ).
74. On sums of triangular numbers, Math.Student, Vol.69,Nos.1-4(2001) 1-6. C.Adiga (with
K.R.Vasuki ).
75. Rogers- Ramanujan identities, continued Fractions, and their Generalizations, Selected
Topics in Special functions, Eds, R.P.Agarwal, H.L.Manocha and K.Srinivasa Rao
(2001),208-226. C.Adiga (with D.D.Somashekara).
76. Strongly *- Graphs, Math. Forum Vol.XIII,(1999-2000), 31-36. C.Adiga (with
D.D.Somashekara).
77. A fixed point theorem in a 2-metric space and an application, J.Nat. and Pht.Sci Vo.15,
Nos.1-2(2001)55-64.C.Adiga (with Giniswamy and S.L.Singh).
78. Contraction type mappings and convergence of sequences of fixed points in 2 -metric
spaces, Proc .National Conf. On challenges of the 21st Century in Mathematics and its
allied topics, (2001), 288-295 C.Adiga (with Giniswamy).
79. On strongly multiplicative graphs, Proc. National Conf. On challenges of the 21st Century
in Mathematics and its allied topics, (2001) 232-235 .C.Adiga (with
H.N.Ramaswamy and D.D.Somashekara).
80. Integral representations and some explicit evaluations of a continued fraction of
Ramanujan, J.P.Jour.Algebra, Number theory and Appl.Vol.2 No.1 (2002),5-20.
C.Adiga(with M.S.Mahadeva Naika and Ramya Rao)
81. On some P-Q eta-function identities of Ramnaujan, Indian Jour. Math. 44 (2002), no.3,
253-267. C.Adiga (with M.S.Mahadeva Naika and K.Shivashankara).
82. A new class of modular equations in Ramanujan's alternative theory of elliptic function of
signature 4 and some new P-Q eta-function identities,Indian Jour. Math.Vol.45, No.1
(2003) 23-27. C. Adiga (With S. Bhargava and M. S. Mahadeva Naika).
83. On Strongly multiplicative graphs, South East Asian J.Math. and Math.Sci,2(2003)
C.Adiga(with D.D.Somashekara and H.N.Ramaswamy ).
84. Transformations of Ramanujan's Summation formula and its applications, JAMA,Vol 1,
No.1 (2005 )55-64.C.Adiga (With T.Kim and N. Anitha )
85. On Ramanujan's Cubic Continued Fraction and Explicit Evaluations of Theta Functions,
Indian J. pure appl. Math. 35(9) (2004 ) 1047-1062. C.Adiga (With T.Kim, M. S.
Mahadeva Naika and H. S. Madhusudan)
86. On a class of N-parity partition, Indian J. Math., No. 2-3, 47(2005 ) 289-293. C.Adiga
(With S. Bhargava and N. Anitha)
87. New Partition theoretic facts of two identities of Euler, Indian J. pure appl. Math. 36(11)
(2005 ) 607-612. C.Adiga (With S. Bhargava and N. Anitha).
88. On an identity of Euler, Journal of Applied Mathematical Analysis and Applications, Vol 2
No.2, (2006), 141-144. C.Adiga (With P. S. Guruprasad).
Page 13
89. A generalization of Agarwal's Theorem, Ramanujan Math. Soc., Lecture Notes series
No.2, (2006), 15-17.C.Adiga (With N. Anitha and Jung Hun Han).
90. General modular transformations for theta-functions, Indian J. Math. 49, No.2, (2007),
239-251. C.Adiga (With M. S. Mahadeva Naika and Jung Hun Han).
91. Strongly quotient graphs, South East Asian J. Math. And Math. Sc., 15 No.2 (2007), 119-
127. C.Adiga (With R. K. Zaferani and M. Smitha).
92. On a three variable reciprocity theorem, South East J. Math. And Math. Sc., Vol 6 No.2
(2008), 57-61. C.Adiga (With P. S. Guruprasad).
93. On modular relations for the functions analogous to Rogers-Ramanujan functions with
applications to partitions, South East J. Math. And Math. Sc., Vol 6 No.2, (2008), 131-
144. C.Adiga (With K. R. Vasuki and B. R. Srivatsa Kumar)..
PROCEEDINGS :
Proceedings of the International Conference on The Works of Srinivasa Ramanujan (2001)
C.Adiga (with D.D.Somashekara)..
No. of Ph. D's guided - submitted : 1
No. of Ph. D's guided - awarded : 6
No. of Ph. D's guided - in progrees : 6
Page 14
DR. D. D. SOMASHEKARA M.Sc ,Ph.D
Designation : Professor of Mathematics
Email id : [email protected]
Phone Number : 9150057505/0821-2419831
Area of Specialization : Special Functions, Number Theory
Research Area : Special Functions, Number Theory, Discrete Mathematics and Graph
Theory
Research Guidance: Special Functions, Number Theory and Graph Theory
No of Publications: 40
List of Publications :
International
1. An estimate of Ramanujan related to the greatest integer function, Bull. Austral. Math.
Soc., Vol. 44, No.1 (1991) 149-154 (with S. Bhargava and C. Adiga).
2. A generalization of Shiokawa’s rational approximations to Rogers-Ramanujan continued
fraction, Comment. Math. Univ. Sancti Pauli, Vol. 41, No.2 (1992), 125-134 (with S.
Bhargava and C. Adiga).
3. Ramanujan’s remarkable summation and an interesting convolution identity, Bull.
Austral. Math. Soc., Vol. 47 (1993), 155-162 (with S. Bhargava and C. Adiga).
4. Three square theorem as an application of Andrews’ identity, Fibonacci Quart., Vol. 31
(1993), 129-133 (with S. Bhargava and C. Adiga).
5. Some eta-function identities deducible from Ramanujan’s 11 summation, J. Math. Anal.
Appl., Vol. 176, No.2 (1993), 554-560 (with S. Bhargava).
6. On the representations of an integer as a sum of a square and thrice a square, Int. J.
Math. Ed. Sci. Tech. Vol. 24, No.3 (1993) 493-496 (with S. Bhargava and C. Adiga).
7. On some Rogers – Ramanujan type continued fraction identities, Mathematica Balkanica,
New Series Vol.12, Nos. 1 – 2 (1998), 37– 45 (with C. Adiga).
8. On a q-analogue of Sandor’s Function, J. Inequal. Pure and Appl. Math. Vol.4, No. 4
(2003) 1-5 (with C. Adiga, T. Kim and Syeda Noor Fathima).
9. A note on strongly multiplicative graphs, Discussiones Mathematicae Graph Theory, Vol.
24 (2004) 81-83 (with C. Adiga and H. N. Ramaswamy).
10. On some generalizations of the Jacobi’s triple product identity, Proceedings of the 15th
International Conference of the Jangjeon Mathematical Society, Edts: S. H. Rim, L. C.
Jang, T. Kim, H. K. Pak, (2004) 32-44.
Page 15
11. On a generalization of Jacobi’s triple product identity and its applications, Adv. Stud.
Contemp. Math., Vol. 9, No.2 (2004) 165-174 (with T. Kim and Syeda Noor Fathima).
12. On transformations of basic bilateral series, Proc. Jangjeon Math. Soc., Vol.8, No.1
(2005) 107-112 (with C. Adiga and Syeda Noor Fathima).
13. Some q-gamma and q-beta function identities deducible from the reciprocity theorem of
Ramanujan, Adv. Stud. Contemp. Math., Vol. 11, No. 2 (2005) 227-234 (with S.
Bhargava and Syeda Noor Fathima).
14. A new convolution identity deducible from the remarkable formula of Ramanujan,
Taiwanese Jour. Math., Vol. 11, No. 2 (2007) 399 – 406 (with S. Bhargava and D.
Mamta).
15. On some arithmetic and real variable functions, Octogon Math. Mag., Vol. 15, No.1
(2007) 63 – 73 (with Jozesf Sandor and D. Mamta).
16. On some identities of Ramanujan found in his lost notebook, Adv. Stud. Contemp.
Math., Vol. 16, No. 2 (2008) 171-180 (with D. Mamta).
17. On Smarandachely harmonic graphs, Int. Jour. Math. Combin., Vol. 4 (2009) 75-83
(with C. R. Veena).
18. A note on three variable reciprocity theorem, Int. J. Pure Appl. Math (2010) (with D.
Mamta).
19. On the skew energy of some unitary Cayley digraphs, Adv. Stud. Contemp. Math., Vol.
20, No. 2 (2010) 261-269 (with C. Adiga, H. N. Ramaswamy and Z. Khoshbakht).
20. On strong vertex graceful graphs. International Mathematical Forum, Vol. 5, No. 56,
(2010) 2751-2757 (with C. R. Veena).
21. On the three variable reciprocity theorem and its applications, The Aust. Jour. Math.
Anal. and Appl. (AJMAA) , Vol. 9, No.1, Art.13(2012) 1-9 (With D. Mamta).
22. On square sum labelings of graphs, Proc. Jangjeon Math. Soc., Vol. 15, No.1 (2012) 69-
78 (with C.R.Veena).
National:
1. On some generalizations of Ramanujan’s continued fraction identities, Proc. Ind. Acad,
Sci., Vol.97 (1987) 31-43 (with S. Bhargava and C. Adiga).
2. On certain continued fractions related to 32 basic hypergeometric functions, Jour. Math.
Sci., Vol. 21, No.6 (1987) 613 – 629 (with S. Bhargava and C. Adiga) .
Page 16
3. Parity results deducible from certain theta function identities found in chapter 16 of
Ramanujan’s second notebook, Math. Student, Vol. 57, Nos. 1-4 (1989) 121-132 (with S.
Bhargava and C. Adiga).
4. Some interesting applications of Ramanujan’s identities to representations of integers as
sums of squares. Presented at 62nd Annual Conference of IMS, held at IIT, Kanpur, during
December 22 – 25, (1996) (with S. Bhargava and C.Adiga).
5. Some relations between infinite series and infinite products, Proceedings of the
symposium on Algebra and Number Theory, Cochin, India, July 27-28, 1990, 23-29. (with
S. Bhargava and C. Adiga)
6. Number of representations of an integer as a sum of a square and five times a square,
Jour. Ind. Math. Soc., Vol.65, Nos. 1-4 (1998), 249 – 251 (with S. Bhargava and C.
Adiga) .
7. Ramanujan’s 11 summation and an interesting generalization of an identity of Jacobi,
Indian J. of Math., Vol. 41, No.1 (1999), 39-42 (with S. Bhargava and C. Adiga).
8. Strongly * graphs, Mathematical Forum, Vol. 8, (1999-2000) 31-36. (with C. Adiga).
9. Rogers – Ramanujan identities, continued fractions and their generalizations, Selected
Topics in Special Functions, Eds: R. P. Agarwal, H.L. Manocha and K. Srinivasa Rao
(2001), 208-226.
(with C. Adiga)
10. Strongly multiplicative graphs, Challenges of the 21st Century in Mathematics and its Allied
Topics: Ed: B. S. Kiranagi (2001), 232-235. (with C. Adiga and H. N. Ramaswamy).
11. An interesting generalization of Jacobi’s triple product identity, Far East J.Math. Sci.
(FJMS), Vol. 9, No. 3 (2003), 255-259. (with Syeda Noor Fathima)
12. On strongly multiplicative graphs, South East Asian J. Math. and Math. Sci. vol.2 (2003)
(with C.Adiga and H. N. Ramaswamy).
13. On continued fraction expansions for the ratios of 22, Indian J. of Math., Vol. 45,
No.3(2003) 333-355 (with Syeda Noor Fathima)
14. A new transformation for basic bilateral hypergeometric series, The Math. Student, Vol.
74, Nos. 1 – 4 (2005) 11 – 29 (with S. Bhargava and Syeda Noor Fathima).
15. On some continued fraction expansions for the ratios of 22, Far East J. Math. Sci. (FJMS),
Vol. 23, No. 1 (2006), 65-80 (with D. Mamta).
16. Interesting generalizations of the additive analogues of the Euler minimum and maximum
functions, South East Asian J. Math. and Math. Sci., Vol. 4, No. 2 (2006) 27 – 32 (with
D. Mamta) .
17. On a two variable reciprocity theorem of Ramanujan, Bull. Pure and Appl. Math., Vol. 5,
No.1 (2011) ( with K. Narasimha Murthy).
Page 17
18. On strongly harmonic graphs. Far East J. Math. Sci. (FJMS), (2012) (to appear) (with C. R.
Veena).
Books Published:
Proceedings of The International Conference on The Works of Srinivasa
Ramanujan (2001) ( With C.Adiga )
No. of Ph. D's guided - awarded : 2
No. of Ph. D's guided - in progress : 3
Page 18
DR. VASUKI K. R. M.Sc ,Ph.D
Designation : Associate Professor
Email id : [email protected]
Phone Number :91-9916450314
Area of Specialization : Number theory and Special function
Research Area : Number theory and Special function
No of Publications: 44
List of Publications :
International
1. On Some New Identities Involving Integrals of Theta-functions, Advanced Studies in
Contemporary Mathematics, 3 (2001), 1-11, with C. Adiga and M. S. M. Naika.
2. Some New Explicit Evaluations of Ramanujan's Cubic Continued Fractions, New Zealand Journal
of Mathematics, 31 (2002), 109-114, with C. Adiga and M. S. M. Naika
3. Some Theta Functions Identities and New Explicit Evaluations of Rogers Ramanujan
Continued Fractions, Tamsui Oxford, J. Mathematical Sciences, 18(1), (2002), 101-117,
with C. Adiga and K. Shivashankara.
4. A Note on Explicit Evaluation of Continued Fraction, Advanced Studies in Contemporary
Mathematics, 9 (2004), 63-80, with T. G. Sreeramamurthy.
5. A Note on P-Q Modular Equations, Tamsui Oxford Journal of Mathematical Sciences, 21(2)
(2005), 109-120, with T. G. Sreeramamurthy.
6. Certain New Ramanujan’s Schlafli Type Mixed Modular Equations, Journal of Mathematical
Analysis and Applications, 309 (2005), 238-255 with T. G. Sreeramamurthy.
7. On Some Ramanujan’s Schalfli Type Modular Equations. Australian Journal of Mathematical
Analysis and Applications, 3(2) (2006), 1-8.
8. Certain Identities for Ramanujan-Gollnitz-Gordon Continued Fraction, Journal of Comp. And
Appl. Math., 187 (2006), 87-95 with B. R Srivatsa Kumar.
9. On 3ψ3 basic Bilateral Hypergeometric Series Summation Formulas, International J. Math.
Combin., 4 (2009), 41-49, with G. Sharath.
10. On a Continued Fraction of Order Six, Ann. Univ. Ferrara, 56 (2010), 77-89, with N. Bhaskar and
G. Sharath.
11. On a Continued Fraction of Order Twelve, Ukranian Mathematical J., 62(12) ( 2010),1609-1619,
with Abdulrawf A. A. Kahtan, G. Sharath and C. Satish Kumar.
Page 19
12. On a 2ψ2 Basic Bilateral Hypergeometric Series Summation Formula, International Math. Form,
5(13-16), (2010), 745-753, with K. R. Rajanna.
13. On Certain New Modular Relations for the Rogers-Ramanujan type functions of Order Twelve,
Advanced Studies in Contemporary Mathematics, 20(3) (2010), 319-333, with P. S. Guruprasad.
14. General Formulas for Evaluation of Singular Modulus of the Complete Elliptic Integral, Advanced
Studies in Contemporary Mathematics, 20(1) (2010), 29-56, with G. Sharath and N. Bhaskar.
15. Two Modular Equations for Squares of the Cubic-Functions with Applications, Note di
Matematica, 30(2) (2010), 61-72, with G. Sharath and K. R. Rajanna.
16. On Certain Theta Function Identities Analogous to Ramanujan’s P-Q Eta-Function Identites,
Applied Mathematics, 2(7) (2011), 874-882, with Abdulrawf A. A. Kahtan.
17. On Some Identities of Ramanujan-Gollnitz-Gordon Continued Fraction, Notes in Number theory
and Discrete Mathematics, 17(4) (2011), 50-60, with G. Sharath and K. R. Rajanna.
18. On the Series Expansion of the Ramanujan Cubic Continued Fraction, International J. Math.
Combin., 4 (2011), 84-95, with Abdulrawf A. A. Kahtan and G. Sharath
19. Some New Modular Relations for the Cubic Functions, Southeast Asian Bulletin of Mathematics (
accepted), with C. Adiga and N. Bhaskar.
National:
1. A Note on Rational Approximation (Presented in the conference), with C. Adiga and D. D.
Somashekara.
2. A Note on Rational Approximations, Journal of Indian Math. Soc., Vol. 65, Nos. 1-4 (1998),
181-189, with C. Adiga.
3. On Some Continued Fractions Related to 22 Basic Bilateral Hypergeometric Seires,
Mathematical Forum, 12, (1998), 31-43.
4. W. N. Bailey's Basic Hypergeometric Series Summation Formula and its Applications, The
Math. Student, 68, (1999), 211-218.
5. A Note on Explicit Evaluations of Products and Ratios of Class Invariants, Mathematical
Forum, Vol. XIII, 1999-2000, 45-56, with K. Shivashankar.
6. Some Explicit Evaluations of Theta-Functions, Far East J. Math. Sci. (FJMS), 2(4) (2000),
625-631, with C. Adiga.
7. Some Evaluations of Rogers - Ramanujan Continued Fraction, Proceedings of the International
Conference on The Works of Srinivasa Ramanujan, Eds: C. Adiga and D. D. Somashekara,
July 1-2, 2000, 209-217, with M. S. M. Naika.
8. Some New Explicit Evaluations of Ratios of Theta-Functions, Proc. Nat. Conf. On Challenges
of the 21th
Century in Mathematics and its Allied topics, University of Mysore, Ed. B. S.
Kirangi, 2001, 253-259, with M. S. M. Naika.
9. On Some Ramanujan's P-Q Identities, Hardy-Ramanujan Journal, 24 (2001) 2-9, with M. S.
M. Naika and H. S. Madhusudhan.
Page 20
10. On Sums of Triangular Numbers, The Math. Student, 70, (2001), 185-190, with C. Adiga.
11. On Some New Continued Fraction Expansions related to 21 Basic Hypergeometric Functions,
Far East J. Math. Sci. (FJMS), 3(3) (2001), 435-443, with Shivashankara K.
12. On Some Continued Fraction Expansions for the Ratios of 22, Special Functions The Aligarh
Bull. of Math., 21 (2002), 25-35 with C. Adiga and Remy Y. Denis.
13. On Certain Continued Fractions Related to 22 Basic Bilateral Hypergeometric Functions,
Indian J. Pure and Appl. Math., 33(10) (2002), 1563-1573, with H. S. Madhusudhan.
14. On Ramanujan's Continued Fractions, Ganitha, 53(1) (2002), 81-88, with K. Shivashankar.
15. Some New Values for the Roger’s-Ramanujan Continued Fraction, J. Indian Math. Soc., 70
(2003), 87-95 with K. Shivashankar
16. Some Evaluations of Ramanujan’s Cubic Continued Fraction, Indian J.pure appl. Math., 35(8)
(2004), 1003-1025, with S. Bhargava and T. G. Sreeramamurthy.
17. Evaluations of Ramanujan-Weber Class Invariant ng , Journal of Indian Math. Soc., 72(1-4)
(2005), 115-127 with S. Bhargava and B. R Srivatsa Kumar.
18. Evalutions of the Ramanujan-Gollnitz-Gordon Continued Fraction H(q) by Modular Equations,
Indian Journal of Mathematics, 48(3) (2006), 275-300 with B. R. Srivatsa Kumar.
19. A note on Ramanujan-Schlafli type mixed modular equations, South east Asian Journal of
Mathematics and Mathematical Sciences, 5(1) (2006), 51-67 with B. R. Srivatsa Kumar.
20. A New Identity for the Roger’s-Ramanujan Continued Fraction, Journal of Applied
Mathematical Anal. And Appl., 2(1) (2006), 71-83 with S. R. Swamy.
21. On Some Ramanujan’s P-Q Modular Equations, J. of Indian Math. Soc., 73 (2006), 131-143.
22. On Certain Ramanujan-Weber type modular equations, J. of Indian Math. Soc, 75 (2008), 173-
192.
23. K. R. Vasuki, P. S. Guruprasad, G. Sharath and C. Chamaraju, On certain new continued
fractions related to 3φ2 basic hypergeometric functions, South east Asian Journal of
Mathematics and Mathematical Sciences, accepted.
24. K. R. Vasuki and C. Chamaraju, A Simple Proof of W. N. Baley’s 2ψ2 Bilateral Basic
Hypergeometric Series Transformation Formula, The Mathematics Student, accepted
25. K. R. Vasuki and T. G. Sreeramurthy, A Note on Rational Approximation of a New
Generalization of the Rogers-Ramanujan Continued Fraction, Mathematical Forum, accepted
Books Published:
No. of Ph. D's guided - awarded : 06
No. of Ph. D's guided - in progress : 05
Page 21
Dr. R. RANGARAJAN M.Sc ,Ph.D
Designation : Associate professor
Email id : [email protected] ,
[email protected]
Phone Number : 0821-2419829/9611109079
Area of Specialization : Pade Approximation, Differential Equations,
Graph Theory
Research Area : Mathematics
Research Guidance : Recognised guide from 06-02-2001
No. of Publications : 41
List of Publication :
International:
1. A Novel Approximate Method for a Nonlinear Heat Transfer Problem,
International J. of Math. Sci. & Engg. Appls., Vol. 5, No.1 (January, 2011), 61-67 (with H. Muneer Basha).
2. Switching Invariant Neighborhood Signed Graphs, Proceedings of the Jangjeon Math. Soc. 14(2) (2011) 249-258 (with P. Siva Kota Reddy and M. S.
Subramanya). 3. Numerical-Analytic Methods for Nonlinear Diffusion Type Differential Equations
of Heat Transfer, Journal of the Indian Math. Soc., Vol. 77, No.s 1-4, (2010), 159-166 (with H. Muneer Basha).
4. The Edge C4 Signed Graph of a Signed Graph, Southeast Asian Bulletin of Mathematics 34(6)(2010) 1077-1082 (with P. Siva Kota Reddy)
5. A Result of Ramanujan and Brahmagupta Polynomials Described by a Matrix Identity, International Journal of Mathematical Combinatorics, International
J. Math. Combin. , Vol.3 (October 2010), 57-63. 6. The H-Line Signed Graph of a Signed Graph, J.Math. Combin., Vol.2 (2010),
37-43 (with P. Siva Kota Reddy and M. S. Subramanya).
7. Notions of balance and consistency on symmetric n-marked graphs, Bul. Pure & Appl. Math, 3(1) (2009), 1-8 (with P. Siva Kota Reddy).
8. Switching Equivalence in Symmetric n-Sigraphs, Adv. Stud. Comtemp. Math. 18(1) (2009), 79-85 (with P. Siva Kota Reddy and M. S. Subramanya).
9. Neighbourhood Signed Graphs, Southeast Asian Bulletin of Mathematics (2009)33: 1-10 (with M. S. Subramanya and P. Siva Kota Reddy)
10. Global Analysis of Lotka-Volterra Predator-Prey Model with Intraspecies competition, Journal of Analysis and Computation, 4.1 (2008): 79-85 (with
M.H. Rahmani Doust). 11. Identity and Non-identity Graphs on n-Sigraphs, International J. of Math. Sci.
& Engg. Appls. 2.3(2008):111-117 (with P. Siva Kota Reddy). 12. Analysis of a Predator-Prey Model with Intraspecies Coexistence, Jour. of
Ultra. Sci. Phy. Sci., 20 (3) (2008)819-824 (with M.H. Rahmani Doust). 13. Notions of Balance in Symmetric n-Sigraphs, Proceedings of the Jangjeon
Math. Soc. 11(2) (2008)145-151 (with P. Siva Kota Reddy).
14. A regular perturbation method for Fisher-Kolmogrov type PDEs, International Journal of Physical Sciences, 19.3M (2007), 503-510 (with Chandrali
Baishya). 15. Perturbation and Painleve analysis for potential KdV and SSD equations,
Journal of Mathematical Analysis and Applications, 3.1 (2007):7-14 (with Chandrali Baishya).
Page 22
16. A perturbation series solution for KdV-Burger equation, Journal of
Mathematical Analysis and Applications, 3.1 (2007):15-21 (with Chandrali Baishya).
17. Geometric models for multiplication of octonions and sedenions, Journal of Analysis and Computation, 3.2 (2007):147-152 (with B. Gayathri Devi).
18. A nonlinear impulsive differential system, International Journal of Physical Sciences, 19.2M (2007), 377-382 (with Hamood A.K. Alhaddad).
19. A nonlinear impulsive integro-differential system I, Journal of Analysis and Computation, 2.2 (2006), 125-131 (with Hamood A.K. Alhaddad).
20. A nonlinear impulsive integro-differential system II, Journal of Analysis and Computation, 2.2 (2006), 133-140 (with Hamood A.K. Alhaddad).
21. A nonlinear impulsive integro-differential system with infinite memory, Journal of Science and Technology, 11.1 (2006), 13-18 (with Hamood A.K.
Alhaddad). 22. The Brahmagupta polynomials extended by generalized golden ratio, Journal
of Mathematical Analysis and Applications, 1.2 (2005), 157-168 (with
Rangaswamy). 23. Orthogonal polynomials of continued fractions and Brahmagupta polynomials,
Journal of Mathematical Analysis and Applications, 1.2 (2005), 169-181 (with Rangaswamy).
24. Brahmagupta Polynomials Arising from the Skew-field of Quaternion, South East Asian Journal of Mathematics and Mathematical Sciences,3.2 (2005),
59-65 (with B. Gayathri Devi) . 25. The Brahmagupta Polynomials in Two Complex Variables and their
Conjugates, The Fibonacci Quarterly, 40.2 (2002), 161-169. (With H.S. Sudheer).
26. The Brahmagupta Matrix and its Application to Tiling, in Special Functions, Proceedings of the International Workshop held at the City University of
Hongkong, June 21-25, 1999. Edited by Charles Dunkl, Mourad Ismail and Roderick Wong. World Scientific, Hongkong (2000), 282-292 (with E.R.
Suryanarayan).
27. Continued Fraction Solutions of Matrix Riccati Equation, In: Mathematical Theory of Control (Proceedings of the International Conference) Edited by M.
C. Joshi and A. V. Balakrishnan, Marcel Dekker, Inc. (1993), 1-10. (With P. Achuthan).
28. On Regular C-fraction and General T-fraction Expansions for Ratios of Basic Hypergeometric Series and Ramanujan-type Identities, Applied Numerical
Mathematics, 12 (1993), 297-313 (with P. Achuthan). 29. On KdV Solitons and Pade’ Approximants, Jour. Math. Phy. Sci, 25(3) (1991),
287-304 (with P. Achuthan and R. Narasimhan) 30. On a Continued Fraction Representation of General Cauer Third Form, Jour.
Math. Phy. Sci, 24(6) (1990), 369-380 (with P. Achuthan).
National :
1. Mathematical Modelling and Computational Aspects of Nonlinear Heat
Transfer Problems, Proceedings of the National Conference on “
Mathematical Modelling: A Socio-Scientific Approach”, Nov. 30, 2011,
Tumkur University(2011).
2. Application of Pade Approximation in solving certain Nonlinear PDEs,
Proceedings of the National Seminar on “Analysis of Partial Differential
Page 23
Equations”, Dec. 18-19, 2009, Ed. Prof. M. Subbiah, Pondicherry
University, Puducherry, (2010),
3. Switching equivalence in symmetric n-Sigraphs. II. J. Orissa Math. Soc. 28 (2009), no. 1-2, 1-12 (with P. Siva Kota Reddy and D.S.
Nandappa) 66-79. 4. Switching invariant 2-path Sigraphs, My Science Vol. 1 (1) (2008), 20-25
(with P. Siva Kota Reddy and M. S. Subramanya). 5. New Perturbation Series Solutions for Fisher’s Equation, Journal of the
Karnataka University, SCIENCE, 43 (2001), 1-11. 6. On a new norm with an important role in computational vedic
mathematics, Proceedings of National Workshop on Computational Vedic Mathematics, ED. K. N. Balasubramanya Murthy and B. S. Ramesh, 39-46
(2002). 7. A Vedic-type Sutra for Approximate Value of N, Applied Science Periodical,
4.3 (2002), 152-158. (With Rangaswamy). 8. On circulant Matrices representing certain directed graphs and magical
semi graphs, Proceedings of the National Seminar on Graph Theory, ED. T.
Thrivikraman, S. Kuriokose and N. Kalayani Kutty, 145-151 (2002). 9. Properties of Brahmagupta Polynomials with two Parameters, Proceedings
of the Third Annual Conference of the Society For Special Functions and their Applications, BHU, Varanasi March 4-6, 2002. Editors R.S.Pathak,
A.K. Agarwal and M.A. Pathan. Society For Special Functions and their Applications (2003), 57-69. (with E.R. Suryanarayan and Rangaswamy).
10. A Continued Fraction Expansion of N Involving a Positive Rational Solution
of x2 –N y2 = -1, Challenges of the 21st century in Mathematics and its
Allied Topics, Proceedings of the National Seminar, University of Mysore, Mysore, February 2-3 2001, Ed. by B.S.Kiranagi University of Mysore
(2001), 224-231. (With Rangaswamy). 11. Sums of Reciprocals Diverging To Infinity Without Hitting Any Integer,
Challenges of the 21st century in Mathematics and its Allied Topics, Proceedings of the National Seminar, University of Mysore, Mysore,
February 2-3 2001, Ed. by B.S.Kiranagi University of Mysore (2001), 236-
241. (With E. R. Suryanarayan). Books Published:
KSOU Course ware, M.Sc Mathematics 2.4, Numerical Analysis, 2011.
No. of Ph. D’s guided - awarded : 07
No. of Ph. D’s guided - in progress : 06
Page 24
DR. H. N. RAMASWAMY M.Sc ,Ph.D
Designation : Professor of Mathematics
Email id : [email protected]
Phone Number : 9449530045/0821-2419832 Area of Specialization : Algebra, Number Theory and Graph Theory. Research Area : Algebraic theory of Quadratic Forms, Number theory and Graph Theory
No of Publications: 10
List of Publications :
1. A note on Euler's totient function, Jour. Ind. Math. Soc. Vol. 62, Nos.1-4 (1996), 169-174 (with C. Adiga).
2. On the Number of Semiorderings over Formally Fields, in Algebra and Its Applications: Proceedings of the International Conference on Algebra and its
Applications, AMU, Aligarh, Narosa Publishing House, (2001) 257- 263.
3. Strongly Multiplicative graphs, in Challenges of the 21st Century in Mathematics and its Allied Topics; Ed: B. S. Kiranagi (2001), 232-235 (with C. Adiga and D.
D. Somashekara).
4. On Strongly Multiplicative Graphs, South East Asian J.Math. and Math. Sc. Vol.2, No.1, 45-47, 2003 (with C. Adiga and D. D. Somashekara).
5. A Note on Strongly Multiplicative Graphs, Discuss. Math. Graph Theory 24 (2004), 81-83 (with C. Adiga and D. D. Somashekara).
6. On S-isotropy and Bani-fields, Proceedings of the Jangjeon Mathematical Society, 8, No.1, (2005) 65 – 72.
7. A note on certain divisibility problem, International Journal of Mathematical Analysis, Vol. 2, no. 21-24, (2008) (with C. Adiga).
8. On the energy of unitary Cayley graphs, The Electronic Journal of Combinatorics, 16 (2009), N24 (with C.R.Veena).
9. On the Skew energy of some unitary Cayley digraphs, Adv. Stud. Contemp.
Math. 20, No.2 (2010) 261-269 (with C. Adiga, D. D. Somashekara, and Z. Khoshbakht).
10. On the Stufe, unit stufe and the Pythagoras number of the ring of
Page 25
integers modulo n, Adv. Stud. Contemp. Math. 20(3) (2010) 273-288. (with
Siddaramu).
Book Published:
1. Math Unlimited: Essays in Mathematics
H.N.Ramaswamy, R.Sujatha, C.S.Yogananda (eds.)
Science Publishers & C R C Press, 2012
No. of Ph. D's guided - awarded : 2
- in progress : 1
