The Energy of Conjugate Graph of a Dihedral Group

Abstract

Let \(\Gamma_{D_{2 n}}^{C}\) and \(E(\Gamma)\) denote the conjugate graph of a dihedral group of order \(2 n(n \in \aleph)\) and the energy of a graph respectively. The sum of the absolute values of the eigenvalues of an adjacency matrix's eigenvalues is the energy of a graph. In this paper, we use group representation of a dihedral group of order 2n with its conjugacy classes to explicitly design admissible conjugate graphs. We further introduced the general formula for the energy of conjugate graphs of dihedral groups in various circumstances. Also, we deduced the general formula for the conjugate graph of generalized dihedral groups of order 2n depending on the nature of n.