On the semitotal dominating sets of graphs

Abstract

A set $D$ of vertices in an isolate-free graph $G$ is a semitotal dominating set of $G$ if $D$ is a dominating set of $G$ and every vertex in $D$ is within distance $2$ from another vertex of $D$.The semitotal domination number of $G$ is the minimum cardinality of a semitotal dominating set of $G$ and is denoted by ${\gamma }_{t2}(G)$. In this paper after computation of semitotal domination number of specific graphs, we count the number of this kind of dominating sets of arbitrary size in some graphs.

10 pages, 2 figures

References in corpus (2)

• On the number of outer connected dominating sets of graphs
• Counting the number of weakly connected dominating sets of graphs