Equality of Domination and Inverse Domination Numbers

Abstract

A set \(D\) of vertices of a graph \(G = (V, E)\) is a \(\textit{dominating set}\) if every vertex of \(V-D\) is adjacent to at least one vertex in \(D\). The \(\textit{domination number}\) \(\gamma(G)\) is the minimum cardinality of a dominating set of \(G\). A subset of \(V-D\), which is also a dominating set of \(G\), is called an \(\textit{averse dominating set}\) of \(G\) with respect to \(D\). The \(\textit{inverse domination number}\) \(\gamma'(G)\) equals the minimum cardinality of an inverse dominating set \(D\). In this paper, we study classes of graphs whose domination and inverse domination numbers are equal.