Exam 3 review Chapter 9- Graphs.

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Chapter 9 Graphs.

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Exam 3 review Chapter 9- Graphs

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 Planar Euler circuit or path possible Other proofs– be able to supply some details, as we do in class on harder problems

Theorems to know for the unit test 9.2: 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) 9.7: Euler: r=e-v+2 Cor 1: connected, planar, simple, e≤ ev-6 Cor 3: no circuits length 3, then e≤2v-4 Thm. 2: A graph is nonplanar iff it contains a subgraph homeomorphic to K3,3 or K5. 9.8: Thm 1- chromatic # of planar graph ≤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