An algorithm and maximum deficiency energy of some graphs

Abstract

The deficiency [Formula: see text] of a vertex [Formula: see text] is the deviation between the degree of the vertex [Formula: see text] and the maximum degree of the graph. The maximum deficiency matrix [Formula: see text] of a simple graph [Formula: see text] is square matrix whose [Formula: see text]th entry is max([Formula: see text], if the vertices [Formula: see text] and [Formula: see text] are adjacent and [Formula: see text], otherwise. Maximum deficiency energy [Formula: see text] is the absolute sum of eigenvalues of maximum deficiency matrix [Formula: see text]. In this paper, we find maximum deficiency energy of some classes of graphs. Moreover, we construct an algorithm and Python 3.8 program to find out spectrum and maximum deficiency energy of [Formula: see text].