THE NIRMALA’S MINIMUM DOMINATING ENERGY OF A GRAPH

Abstract

Nirmala index is one of the recently discovered topological index. It is originally a vertex based topological invariant and is defined as the sum of \(\sqrt{d(r)+d(s)}\)  terms on all  edges of the graph, where  \(d(r)\) is the degree of the vertex \(r\) in \(G\) . In this paper we put forward a new energy called as the nirmala minimum dominating energy of a graph \(N E_{D}(G)\) . Also, we compute  \(N E_{D}(G)\) for cocktail party graph, star graph, complete bipartite graph and complete graph. The estimation of upper and lower bounds for \(N E_{D}(G)\) are found.