### $Y \overline{Y}$ 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.

#### Keywords

$Y\overline{Y}$-dominating set; $Y$-dominating set; $X$-dominating set

#### Full Text:

PDFDOI: http://dx.doi.org/10.26713%2Fjims.v4i1.64

eISSN 0975-5748; pISSN 0974-875X