a4-10-8

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

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
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
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 07/13/2011 for the course MAD 2104 taught by Professor Staff during the Spring '08 term at FAU.

Page1 / 5

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

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online