Degree square subtraction energy of non-commuting graph for dihedral groups

Abstract

The non-commuting graph on a finite G, denoted by ΓG, with the set of non-central elements of G as the vertex set and two distinct vertices are adjacent whenever they do not commute in G. In this paper, we discuss the spectrum, spectral radius and degree square subtraction energy of ΓG for dihedral groups of order 2n, D2n , where n≥3. It is found that the obtained energy here is equal to twice its spectral radius and there is a relationship with the degree subtraction energy that was described in previous literature.