| Abstract |
In this paper, we introduce and initiate the study of outer-connected semitotal domination in graphs. Given a graph $G$ without isolated vertices, a set $S$ of vertices of $G$ is a semitotal dominating set if every vertex outside of $S$ is adjacent to a vertex in $S$ and every vertex in $S$ is of distance at most 2 units from another vertex in $S$. A semitotal dominating set $S$ of $G$ is an outer-connected semitotal dominating set if either $S=V(G)$ or $Sneq V(G)$ satisfying the property that the subgraph induced by $V(G)setminus S$ is connected. The smallest cardinality $tilde{gamma}_{t2}(G)$ of an outer-connected semitotal dominating set is the outer-connected semitotal domination number of $G$. First, we determine the specific values of $tilde{gamma}_{t2}(G)$ for some special graphs and characterize graphs $G$ for specific (small) values of $tilde{gamma}_{t2}(G)$. Finally, we investigate the outer-connected semitotal dominating sets in the join, corona and composition of graphs and, as a consequence, we determine their respective outer-connected semitotal domination numbers. |
Mindanao State
University - Iligan Institute of Technology