Some new perspectives on global domination in graphs (Q361579)

Summary: A dominating set is called a global dominating set if it is a dominating set of a graph \(G\) and its complement \(\overline{G}\). Here we explore the possibility to relate the domination number of graph \(G\) and the global domination number of the larger graph obtained from \(G\) by means of various graph operations. In this paper we consider the following problem: Does the global domination number remain invariant under any graph operations? We present an affirmative answer to this problem and establish several results.