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Exam 3 review

Exam 3 review. Chapter 10- Graphs. Basics and proofs to know well. Special graphs: K n , C n , W n , Q n , K m,n Use these for calculations, counterexamples… Know the definitions of bipartite, isomorphic, and planar Prove : Bipartite or not Isomorphic or not Planar or not

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Exam 3 review

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  1. Exam 3 review Chapter 10- Graphs

  2. Basics and proofs to know well • Special graphs: Kn, Cn, Wn, Qn, Km,n • Use these for calculations, counterexamples… • Know the definitions of bipartite, isomorphic, and planar • Prove: • Bipartite • or not • Isomorphic • or not • Planar • or not • Euler circuit or path possible • or not • Other proofs– be able to supply some details, as we do in class on harder problems

  3. Theorems to know for the unit test • 10.2: Thm. 1 Handshaking: 2e= sum of deg(v) • Thm. 2: undirected graph has an even # of odd degree • Conditions for when an Euler path or circuit exist (don’t worry about Hamilton conditions) • 10.7: Euler: r=e-v+2 • Cor 1: connected, planar, simple, e≤ ev-6 • Cor3: no circuits length 3, then e≤2v-4 • Thm. 2: A graph is nonplanariff it contains a subgraphhomeomorphic to K3,3or K5. • 10.8: Thm 1- chromatic # of planar graph ≤4

  4. Calculations to do • Calculate deg, deg-, deg+ • Adjacency tables and matrices • Paths • Strong and weakly connected • Counting paths of a certain length l • Euler and Hamilton paths and circuits • Conditions for Euler paths and circuits (not for Hamilton) • Chromatic number of special graphs

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