arXiv subjects

Ismael Rios-Villamar

Publications and source records attributed to Ismael Rios-Villamar.

2 recordsLinked to original sources

arXiv2026

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

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.

math.CO↗

arXiv2026

Independent domination in central graphs

Let $G$ be a graph with vertex set $V(G)$. A set $I\subseteq V(G)$ is an independent dominating set of $G$ if no two vertices in $I$ are adjacent and every vertex in $V(G)\setminus I$ is adjacent to at least one vertex in $I$. The independent domination number of $G$ is the minimum cardinality among all independent dominating sets of $G$. The aim of this article is to obtain tight bounds and closed formulas for the independent domination number of central graphs. The results are expressed in terms of parameters of the original graph from which the central graph is constructed.

math.CO↗