On the semitotal dominating sets of graphs

Document Type : Research Paper

Authors

Department of Mathematical Sciences, Yazd University, Yazd, Iran

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.

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Journal of Algebra and Related Topics
Volume 12, Issue 2
January 2025
Pages 37-46

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