The Minimum Paired Dominating Energy of a Graph

Abstract

Let $G$ be any graph. A dominating set $D$ in $G$ is called a paired dominating set if $\langle D \rangle$ contains a perfect matching. The minimum cardinality of a paired-dominating set is called the paired-domination number, denoted by $\gamma_{pd} (G)$. In this paper, we study the minimum paired dominating energy $E_{pd}(G)$, exact value of $E_{pd}(G)$ is calculated for some standard graphs. Further, the bounds are established for $E_{pd}(G)$.