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CSE 321 Discrete Structures

Dive into the world of graphs with applications in social networks, web structures, and communication networks. Explore special graphs, colorability, representations, connectivity, paths, and isomorphism concepts.

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CSE 321 Discrete Structures

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

  2. Announcements • Readings • This week • 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?

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