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Lecture 11 CSE 331 Sep 25, 2009 Homeworks Please hand in your HW 2 now HW 3 and graded HW 1 at the end of class Graphs Representation of relationships between pairs of entities/elements # vertices = n #edges = m Edge Vertex Paths , Sequence of (distinct) vertices connected by edges Connected Path length 3 , , , Connected Graphs Every pair of vertices has a path between them Cycles Sequence of k vertices connected by edges, first k-1 are distinct , , , Tree Connected undirected graph with no cycles Rooted Tree A rooted tree How many rooted trees can an n vertex tree have? Pick any vertex as root Let the rest of the tree hang under “gravity” SG’s parent=AC AC’s chil d=S G 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 2n such sequences Check if any is a path between s and t Algorithm motivation all