Degree Square Subtraction Energy of Non-Commuting Graph for Dihedral Groups

The non-commuting graph on a finite , denoted by , with the set of non-central elements of as the vertex set and two distinct vertices are adjacent whenever they do not commute in . In this paper, we discuss the spectrum, spectral radius and degree square subtraction energy of for dihedral groups of order , where . 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.