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MIT6_042JS10_lec16

MIT6_042JS10_lec16 - Types of Graphs Mathematics for...

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1 Albert R Meyer, March 10, 2010 lec 6W.1 Mathematics for Computer Science MIT 6.042J/18.062J Simple Graphs Degrees, Isomorphism, Paths Albert R Meyer, March 10, 2010 lec 6W.2 Types of Graphs Directed Graph Multi-Graph Simple Graph this week next week Albert R Meyer, March 10, 2010 A simple graph: Definition: A simple graph G consists of •a nonempty set, V, of vertices •a set, E, of edges (edge = set of 2 vertices) lec 6W.3 Albert R Meyer, March 10, 2010 lec 6W.5 vertices, V undirected edges, E A Simple Graph ::= { , } edge “adjacent Albert R Meyer, March 10, 2010 deg( ) = 2 lec 6W.9 degree of a vertex is # of incident edges Vertex degree Albert R Meyer, March 10, 2010 lec 6W.10 degree of a vertex is # of incident edges Vertex degree deg( ) = 4
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2 Albert R Meyer, March 10, 2010 lec 6W.11 orphaned edge Is there a graph with vertex degrees 2,2,1? NO! 2 2 1 Im possible Graph Albert R Meyer, March 10, 2010 lec 6W.12 sum of degrees is twice # edges Handshaking Lemma Proof : Each edge contributes 2 to the sum on the right Albert R Meyer, March 10, 2010 lec 6W.13 Handshaking Lemma sum of degrees is twice # edges 2+2+1 = odd, so impossible Albert R Meyer, March 10, 2010 lec 6W.14 Sex in America: Men more Promiscuous? Study claims: Men average many more partners than women.
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