Domination in Graphs: A Brief Overview

Abstract

In a graph $G=(V,E)$, a set $S\subset V$ is a dominating set if each vertex of $V–S$ is adjacent to at least one vertex in $S$.Approximately 1000 papers have been written on domination-related concepts, with more than half of them appearing in the literature in the last five years. Obviously, a comprehensive survey is beyond the scope of this paper, so a brief overview is presented.