The Minimum Maximal Domination Energy of a Graph

Abstract

Small A dominating set $D$ of a graph $G$ is maximal if $V-D$ is not a dominating set of $G$. The maximal domination number $\gamma_m(G)$ of G is the minimum cardinality of a maximal dominating set in $G$. In this paper, we are introduced minimum maximal domination energy $E_{D}(G)$ of a graph $G$. We are computed minimum maximal domination energies of some standard graphs and a number of well-known families of graphs. Upper and lower bounds for $E_{D}(G)$ are established.