Deficiency Sum Energy of Some Graph Classes

In this paper, we introduce the concept of deficiency sum matrix Sdf (G) of a simple graph G = (V;E) of order n. The deficiency df(v) of a vertex v 2 V is the deviation between the degree of the vertex v and the maximum degree of the graph. The deficiency sum matrix Sdf (G) is a matrix of order n whose (i; j)-th entry is df(vi) + df(vj), if the vertices vi and vj are adjacent and 0, otherwise. In addition, we introduce deficiency sum energy ESdf (G) of a graph G and establish some bounds for ESdf (G). Further, deficiency sum energy of some classes of graphs are obtained. Moreover, we construct an algorithm and python(3.8) code to find out spectrum and deficiency sum energy of graph G.