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Lecture 11
CSE 331Sep 25, 2009
Homeworks
Please hand in your HW 2 now
HW 3 and graded HW 1 at the end of class
GraphsRepresentation of relationships between pairs of entities/elements
VertexVertex
EdgeEdge
# vertices = n
#edges = m
# vertices = n
#edges = m
Paths
Sequence of (distinct) vertices connected by edges
, , ,
Path length 3Path length 3
,
ConnectedConnected
Connected Graphs
Every pair of vertices has a path between them
Cycles
Sequence of k vertices connected by edges, first k-1 are distinct
, , ,
TreeConnected undirected graph with no cycles
Rooted Tree
A rooted tree
Pick any vertex as root
Let the rest of the tree hang under “gravity”
How many rooted trees
can an n vertex tree
have?
How many rooted trees
can an n vertex tree
have?
SG’s parent=AC
SG’s parent=AC
AC’s child=SG
AC’s child=SG
Rest of Today’s agenda
Prove n vertex tree has n-1 edges
Algorithms for checking connectivity
Checking by inspection
What about large graphs?
s
t
Are s and t connected?
Brute-force algorithm?
List all possible vertex sequences between s and t
Check if any is a path between s and t
2n such sequences
2n such sequences
Algorithm motivation
allall