Nonsplit pendant domination in graphs

Abstract

For a graph $G$, a dominating set $S$ in $G$ is called a pendant dominating set if $\langle S \rangle$ contains at least one pendant vertex. The least cardinality of the pendant dominating set in $G$ is called the pendant domination number of $G$, denoted by $\gamma_{pe}(G)$. A pendant dominating set $S$ of a graph $G$ is a nonsplit pendant dominating set if the induced graph $<V-S>$ is connected. The nonsplit pendant domination number $\gamma_{nsp}(G)$ is the minimum cardinality of a nonsplit pendant dominating set. In this paper many bounds on $\gamma_{nsp}(G)$ are obtained and exact values for some standard graphs are found. Also, its relationship with other parameters has been investigated.