1. CSE 321 Discrete Structures
Winter 2008
Lecture 26
Graph Theory

2. Announcements Readings Schedule This week Quiz Section, Thursday
Graph Theory, 9.1 – 9.4
Schedule
Quiz Section, Thursday
No class Friday.
Review Session, Sunday, 2pm
Final Exam, Monday, March 17

3. Highlights from Lecture 25
Graph Theory
Graph Applications
Facebook Graph
Web Graph
Communication Graphs a b a b
V = {a, b, c}
E = {{a,b}, {b,c}}
V = {a, b, c}
E = {<a,b>, <c,b>} c c

4. Handshake Theorems

5. Special Graphs
Complete Graphs Kn
Cycle Cn
Hypercube Qn
Mesh Mn,m

6. Bipartite Graphs

7. 2-coloring
A graph is two colorable iff all cycles have even length

8. Graph Representations
Adjacency Lists
Adjacency Matrices
Incidence Matrices

9. Graph Connectivity

10. Strong connectivity vs. Weak Connectivity

11. Strongly Connected Components

12. Counting Paths
Let A be the Adjacency Matrix. What is A2? b a c d e

13. Graph Isomorphism I
Are these two graphs the same? y a d x w b c z

14. Graph Isomorphism II
Are these graphs the same?

15. Graph Isomorphism III
Are these graphs the same?