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arXiv · 2609.33932

On the (independent) semitotal domination in subdivision, middle, and central graphs

Abel Cabrera-Martínez·José Luis López-Carmona·Ismael Rios-Villamar·Alejandro Serrano-Díaz
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Abstract

A dominating set $D$ of a nontrivial connected graph $G$ is called a semitotal dominating set of $G$ if every vertex in $D$ is at distance at most two from another vertex in $D$. If, in addition, $D$ is an independent set, then $D$ is called an independent semitotal dominating set of $G$. The (independent) semitotal domination number of $G$ is the minimum cardinality among all (independent) semitotal dominating sets of $G$. In this paper, we obtain closed formulas for these parameters in the following three well-known graph operators defined from a connected graph: the subdivision, middle, and central graphs.

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Abel Cabrera-Martínez, José Luis López-Carmona, Ismael Rios-Villamar, Alejandro Serrano-Díaz. 2026-09-27. On the (independent) semitotal domination in subdivision, middle, and central graphs. https://arxiv.org/abs/2609.33932

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