Misbalance degree matrix and related energy of graphs

Abstract

Given a graph G = (V,E), the Misbalance deg (MD) index of G is defined as MD(G) = ∑|du−dv|, where E is the set of edges of G, and du be the degree of the vertex u ∈ V, set of vertices of G. A modification of the classical adjacency matrix of a graph is propose based on MD index and its spectra is studied in connection with subdivision, semitotal point graph, semitotal line graph, and total graphs of a regular graph. Analogously two new concepts namely MD energy and MD estrada index are also coined