DEGREE EXPONENT SUM ENERGY OF COMMUTING GRAPH FOR DIHEDRAL GROUPS

Abstract

For a finite group G and a nonempty subset X of G, we construct a graph with a set of vertex X such that any pair of distinct vertices of X are adjacent if they are commuting elements in G. This graph is known as the commuting graph of G on X, denoted by ΓG [X]. The degree exponent sum (DES) matrix of a graph is a square matrix whose (p,q)-th entry is is dvp dvq + dvqdvp whenever p is different from q, otherwise, it is zero, where dvp (or dvq ) is the degree of the vertex vp (or vertex, vq) of a graph. This study presents results for the DES energy of commuting graph for dihedral groups of order 2n, using the absolute eigenvalues of its DES matrix.