1. Lecture 11 CSE 331 Sep 25, 2009

2. Homeworks Please hand in your HW 2 now HW 3 and graded HW 1 at the end of class

3. Graphs Representation of relationships between pairs of entities/elements Vertex Edge # vertices = n #edges = m # vertices = n #edges = m

4. Paths Sequence of (distinct) vertices connected by edges,,, Path length 3, Connected

5. Connected Graphs Every pair of vertices has a path between them

6. Cycles Sequence of k vertices connected by edges, first k-1 are distinct,,,

8. Tree Connected undirected graph with no cycles

9. Rooted Tree

10. 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? SG’s parent=AC AC’s chil d=S G

11. Rest of Today’s agenda Prove n vertex tree has n-1 edges Algorithms for checking connectivity

12. Checking by inspection

13. What about large graphs? s t Are s and t connected?

14. Brute-force algorithm? List all possible vertex sequences between s and t Check if any is a path between s and t 2 n such sequences

15. Algorithm motivation all