\(Y\overline{X}\) domination in bipartite graphs

Abstract

A subset \(S\) of \(X\) is called a \(Y\overline{X}\) dominating set if \(S\) is a \(Y-\)dominating set and \(X - S\) is not a \(X\)-dominating set. A subset \(S\) of \(X\) is called a minimal \(Y\overline{X}\) dominating set if any proper subset of \(S\) is not a \(Y\overline{X}\) dominating set. The minimum cardinality of a minimal \(Y\overline{X}\) dominating set is called the \(Y\overline{X}\) domination number of \(G\) and is denoted by \(\gamma_{Y\overline{X}}(G)\). In this paper some results on \(Y\overline{X}\) domination number are obtained.