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Discrete Mathematics and its Applications
Found in: Page 738
Discrete Mathematics and its Applications

Discrete Mathematics and its Applications

Book edition 7th
Author(s) Kenneth H. Rosen
Pages 808 pages
ISBN 9780073383095

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Short Answer

A dominating set of vertices in a simple graph is a set of vertices such that every other vertex is adjacent to at least one vertex of this set. A dominating set with the least number of vertices is called a minimum dominating set. Find a minimum dominating set for the given graph.

The minimum dominating set for the graph is \(\left\{ {c,d} \right\}\).

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Step by Step Solution

TABLE OF CONTENTS :
TABLE OF CONTENTS

Step 1: Concept/Significance of a minimum dominating set

A minimum dominating set is one that isn't a legitimate subset of some other dominating set in a graph. The domatic number of a graph can be calculated with minimal dominant sets.

Step 2: Determination of the minimum dominating set in the graph

As each of the other vertices, a, b, e, and f, is next to at least one of the cords,c and d,\(\left\{ {c,d} \right\}\) is the smallest dominating set, implying that there is no other smaller dominating set.

Thus, the minimum dominating set for the given graph is \(\left\{ {c,d} \right\}\).

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