1. Lecture 11
CSE 331
Sep 23, 2011

2. HW 2 due today I will not take any HW after 1:15pm
Q2, Q3 and Q4 in different piles
I will not take any HW after 1:15pm

3. Solutions to HW 2
Handed out at the END of the lecture

4. HW 3
Has been posted (link on the blog)
Start early

5. Graded HW 1
Pick up from recitation/TA office hours next week

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

7. Paths , , Sequence of vertices connected by edges Connected
Path length 3 ,

8. Connectivity
u and v are connected iff there is a path between them
A graph is connected iff all pairs of vertices are connected

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

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

12. Puzzle # 3 How many distinct graphs on n vertices?
How many distinct trees on n vertices?

13. HW 2 due today I will not take any HW after 1:15pm
Q1, Q2 and Q3 in different piles
I will not take any HW after 1:15pm

14. Tree
Connected undirected graph with no cycles

15. Rooted Tree

16. How many rooted trees can an n vertex tree have?
A rooted tree
How many rooted trees can an n vertex tree have?
AC’s child=SG
Pick any vertex as root
SG’s parent=AC
Let the rest of the tree hang under “gravity”

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

18. Checking by inspection

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

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

21. Algorithm motivation
all