THE NIRMALA’S MINIMUM DOMINATING ENERGY OF A GRAPH
B. K. DIVYASHREE *
Department of Mathematics, Government Science College, Bangalore, 560056, India.
R. JAGADEESH
Department of Mathematics, Government First Grade College, Ramanagara, 562120, India.
. SIDDABASAPPA
Department of Mathematics, Government Science College, Bangalore, 560056, India.
*Author to whom correspondence should be addressed.
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.
Keywords: Nirmala energy, nirmala’s minimum dominating energy, cocktail party graph, star graph, complete bipartite graph and complete graph