## Graphs with Equal Domination and Independent Domination Number

## Graphs with Equal Domination and Independent Domination Number

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*S. K. Vaidya, R. M. Pandit*

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## Abstract

A set S of vertices of a graph G is an independent dominating set of G if S is an independent set and every vertex not in S is adjacent to a vertex in S. The independent domination number of G, denoted by i(G), is the minimum cardinality of an independent dominating set of G. In this paper, some new classes of graphs with equal domination and independent domination numbers are presented and exact values of their domination and independent domination numbers are determined.

## Keywords

Dominating set, domination number, independent dominating set, indepenĀ¬dent domination number.