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.

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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