Let G = (V, E) be a graph. A subset D of V is called dominating if for all v ∈ V, either v ∈D or v is adjacent to some vertex in D. If D is a dominating set, and no proper subset of D is a dominating set, then D is called minimal. If G has no isolated vertices, prove that if D is a minimal dominating set for G, then V – D is a dominating set for G.

Let G = (V, E) be a graph. A subset D of V is called dominating if for all v ∈ V, either v ∈D or v is adjacent to some vertex in D. If D is a dominating set, and no proper subset of D is a dominating set, then D is called minimal. If G has no isolated vertices, prove that if D is a minimal dominating set for G, then V – D is a dominating set for G.

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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