Domination in Graphs: A Brief Overview

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.