A graph is called k regular if k edges meet at each vertex Let G be a k regular graph (a) Show that the adjacency matrix A of G has k as an eigenvalue (b) Show that if A is primitive, then the other eigenvalues are all less than k in absolute value ...

a Each column of A sums to k since each vertex connects to k others Thus A kP ...

A graph is called k-regular if k edges meet at each vertex. Let G be a k-regular

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A graph is called k-regular if k edges meet at each vertex. Let G be a k-regular graph.
(a) Show that the adjacency matrix A of G has λ = k as an eigenvalue.

(b) Show that if A is primitive, then the other eigenvalues are all less than k in absolute value.

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Linear Algebra A Modern Introduction

ISBN: 978-0538735452

3rd edition

Authors: David Poole

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Question Posted: Nov 13, 2018 11:13 AM

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A graph is called k-regular if k edges meet at each vertex. Let G be a k-regular

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Linear Algebra A Modern Introduction

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