Some New Results on Seidel Equienergetic Graphs

Abstract

The energy of a graph G is the sum of the absolute values of the eigenvalues of the adjacency matrix of G. Some variants of energy can also be found in the litera- ture, in which the energy is de_ned for the Laplacian matrix, Distance matrix, Common- neighbourhood matrix or Seidel matrix. The Seidel matrix of the graph G is the square matrix in which ijth entry is 􀀀1 or 1, if the vertices vi and vj are adjacent or non-adjacent respectively, and is 0 , if vi = vj . The Seidel energy of G is the sum of the absolute values of the eigenvalues of its Seidel matrix. We present here some families of pairs of graphs whose Seidel matrices have di_erent eigenvalues, but who have the same Seidel energies.