Copyright © 2012 T. Tamizh Chelvam and T. Asir. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

A subset D of the vertex set of a graph G, is a dominating set if every vertex in is adjacent to at least one vertex in D. The domination number is the minimum cardinality of a dominating set of G. A subset of , which is also a dominating set of G is called an inverse dominating set of G with respect to D. The inverse domination number is the minimum cardinality of the inverse dominating sets. Domke et al. (2004) characterized connected graphs G with , where n is the number of vertices in G. It is the purpose of this paper to give a complete characterization of graphs G with minimum degree at least two and .