Answered: (d) Suppose that a graph G is regular… | bartleby

Linear Algebra: A Modern Introduction

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter2: Systems Of Linear Equations

Section2.4: Applications

Problem 32EQ

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Help with no (d) please

(a) Write down the chromatic number of each of the graphs below. Justify your answer by
colouring the graph.
(i) Cube.
(ii) Krst
(iii) Wn
01 120
1000 1
(b) A graph G has adjacency matrix A =
10011
20.100
0 1 10 0
(i) Is Ga simple graph?
(i) Write down the degree sequence for G.
(c) Prove by induction that the number of edges of K, is 01-1).
2
(d) Suppose that a graph G is regular of degree r, where r is odd.
(i) Prove that G has an even number of vertices.
(ii) Prove that the numof G is a multiple of r.
(e) A simple graph has 20 vertices. Any two distinct vertices u and v are such that
deg(u) + deg(v) 2 20. Prove by contradiction that the graph is connected.
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