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 |. 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|.

Part(a): Assume that I is an independent set of G. If possible suppose that V-I is not a vertex…

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 |.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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