Independent set dominating sets in bipartite graphs

Abstract

The paper continues the study of independent set dominating sets in graphs which was started by E. Sampathkumar. A subset $D$ of the vertex set $V(G)$ of a graph $G$ is called a set dominating set (shortly sd-set) in $G$, if for each set $X \subseteq V(G)-D$ there exists a set $Y \subseteq D$ such that the subgraph $X \cup Y$ of $G$ induced by $\langle X \cup Y\rangle$ is connected. The minimum number of vertices of an sd-set in $G$ is called the set domination number $\gamma_s(G)$ of $G$. An sd-set $D$ in $G$ such that $|D|=\gamma_s(G)$ is called a $\gamma_s$-set in $G$. In this paper we study sd-sets in bipartite graphs which are simultaneously independent. We apply the theory of hypergraphs.