The Global Maximal Domination Number of a Graph

Abstract

A maximal dominating set D of a graph G is a global maximal dominating set if D is also a maximal dominating set of $\bar{G}$. The global maximal domination number $\gamma_{gm}(G)$ of G is the minimum cardinality of a global maximal dominating set. In this paper, bounds for $\gamma_{gm}(G)$ and exact values of $\gamma_{gm}(G)$ for some standard graphs are obtained. We characterize maximal dominating sets of G which are global maximal dominating sets. Also Nordhaus-Gaddum type results are obtained.