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 defined 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 different eigenvalues, but who have the same Seidel energies.
