KYUNGPOOK Math. J. 2019; 59(2): 335-340
Published online June 23, 2019
Copyright © Kyungpook Mathematical Journal.
Some New Results on Seidel Equienergetic Graphs
Samir K. Vaidya∗, Kalpesh M. Popat
Department of Mathematics, Saurashtra University, Rajkot-360005, Gujarat, India
e-mail : samirkvaidya@yahoo.co.in
Department of Master of Computer Application, Atmiya Institute Of Technology & Science, Rajkot-360005, Gujarat, India
e-mail : kalpeshmpopat@gmail.com
Received: March 30, 2018; Revised: April 27, 2019; Accepted: May 10, 2019
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 literature, 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.