Unformatted text preview: 1. [BB] Here is one possibility. v'6 v , V5 V4 Vl V2 Vl V2 Vl V2 GE) \ 0 0 /., o V3 V3 2. o V3 o edges; 0, 0, 0 1 edge; 1, 1,0 1 edge; 1, 1,0 1 edge; 1, 1, 0 Vl V2 Vl V2 Vl V2 \: v: \1., 2 edges; 2, 1, 1 2 edges; 2, 1, 1 2 edges; 2, 1, 1 3 edges; 2, 2,2 The question doesn't make sense for pseudographs because we could just keep adding edges indefinitely. 3. [BB] o 4. (a) There are six vertices, 12 edges and the degree sequence is 6, 5, 4, 4, 3, 2. (b) Proposition 9.2.5: L: deg Vi = 6 + 5 + 4 + 4 + 3 + 2 = 2(12) = 21t"lCorollary 9.2.6: There are two odd vertices (of degrees 3 and 5), two being even. 5. [BB] 10 edges. This is JC 5 , the complete graph on five vertices....
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 Summer '10
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 Graph Theory, Vertex, Vl V2

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