The Minimum Boundary Dominating Energy of a Graph

Abstract

For a graph G, a subset $ B $ of $ V(G) $ is called a boundary dominating set if every vertex of $ V(G)- S $ is vertex boundary dominated by some vertex of $ S $. The boundary domination number $\gamma_{b}(G)$ of G is the minimum cardinality of minimum boundary dominating set in G. In this paper we introduce the minimum boundary dominating energy $E_{B}(G)$ of a graph G and computed minimum boundary dominating energies of some standard graphs. Upper and lower bounds for $E_{B}(G)$ are established.