An independent set of a graph G is a subset I of the vertex set V such that no twovertices in I are adjacent. Let i(G) be the size of a maximal independent set of G.(a) Show that I is an independent set of G if and only if V − I is a vertex coverof G.(b) Conclude from part (a) that i(G) + vc(G) = |V |. 3. An independent set of a graph G is a subset I of the vertex set V such that no twovertices in I are adjacent. Let i(G) be the size of a maximal independent set of G.(a) Show that I is an independent set of G if and only if V – I is a vertex coverof G.(b) Conclude from part (a) that i(G) + vc(G) = |V|.

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An independent set of a graph G is a subset I of the vertex set V such that no two vertices in I are adjacent. Let i(G) be the size of a maximal independent set of G. (a) Show that I is an independent set of G if and only if V – I is a vertex cover of G. (b) Conclude from part (a) that i(G) + vc(G) = |V|.

An independent set of a graph G is a subset I of the vertex set V such that no two vertices in I are adjacent. Let i(G) be the size of a maximal independent set of G. (a) Show that I is an independent set of G if and only if V – I is a vertex cover of G. (b) Conclude from part (a) that i(G) + vc(G) = |V|.

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter3: Matrices

Section3.7: Applications

Problem 74EQ

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