$Y \overline{Y}$ Domination in Bipartite Graphs

Abstract

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