Independent domination in central graphs

Abstract

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.