a4-10-8

a4-10-8 - Section 46 1 Write the graphs whose pictures...

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1. Write the graphs whose pictures appear in the text as pairs of sets ( V; E ) . (a) ( f 1 ; 2 ; 3 ; 4 ; 5 ; 6 g ; ff 1 ; 2 g ; f 1 ; 4 g ; f 2 ; 3 g ; f 2 ; 5 g ; f 3 ; 6 g ; f 4 ; 5 g ; f 5 ; 6 gg ) (b) ( f 1 ; 2 ; 3 ; 4 ; 5 ; 6 g ; ff 1 ; 2 g ; f 1 ; 4 g ; f 1 ; 6 g ; f 2 ; 3 g ; f 2 ; 5 g ; f 3 ; 4 g ; f 4 ; 5 g ; f 4 ; 6 g ; f 5 ; 6 gg ) (c) ( f 1 ; 2 ; 3 ; 4 ; 5 ; 6 g ; ff 1 ; 2 g ; f 1 ; 4 g ; f 2 ; 5 g ; f 4 ; 5 gg ) 2. Draw pictures of (a) ( f a; b; c; d; e g ; ff a; b g ; f a; c g ; f a; d g ; f b; e g ; f c; d gg ) e e e e e c a b e d (b) ( f a; b; c; d; e g ; ff a; b g ; f a; c g ; f b; c g ; f b; d g ; f c; d gg ) e e e e e ± ± ± ± ± ± a b d e c (c) ( f a; b; c; d; e g ; ff a; c g ; f b; d g ; f b; e gg ) e e e e e a c d b e 12. Let G be a graph. Prove that there must be an even number of vertices of odd degree . If there were an odd number of vertices with odd degree, then the sum of the degrees of all the vertices would be odd. But Theorem 46.5 says
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a4-10-8 - Section 46 1 Write the graphs whose pictures...

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