Deficiency Sum Energy of Some Graph Classes

In this paper, we introduce the concept of deficiency sum matrix S-df (G) of a simple graph G = (V, E) of order n. The deficiency df(v) of a vertex v is an element of V is the deviation between the degree of the vertex v and the maximum degree of the graph. The deficiency sum matrix S-df(G) is a matrix of order n whose (i, j)-th entry is df(v(i)) + df(v(j)), if the vertices v(i) and v(j) 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. (C) 2023 University of Kashan Press. All rights reserved.