On the distance spectrum and distance energy of complement of subgroup graphs of dihedral group

Abstract

Let G is a connected simple graph and V(G) = {v 1 , v 2 , ..., v p } is vertex set of G. The distance matrix of G is a matrix D(G) = [d ij ] of order p where [d ij ] = d(v i , v j ) is distance between v i and v j in G. The set of all eigenvalues of matrix D(G) together with their corresponding multiplicities is named the distance spectrum of G and denoted by spec D (G). The distance energy of G is , where λ i are eigenvalues of D(G). In the recent paper, the distance spectrum and distance energy of complement of subgroup graphs of dihedral group are determined.