Graphs with equal domination and independent domination number

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.Publisher's Versio

On graphs with equal domination and independent domination numbers

AbstractAllan and Laskar have shown that K1.3-free graphs with equal domination and independent domination numbers. In this paper new classes of graphs with equal domination independent domination numbers.are presented. In particular, the result of Allan and Laskar is generalized