On the Estrada Index of Seidel Matrix

Document Type : Original Scientific Paper

Authors

Department of Mathematics, Faculty of Science, Shahid Rajaee Teacher Training University, Tehran

Abstract

Let G be a simple graph with n vertices and with the Seidel matrix S‎. ‎Suppose μ1‎, ‎μ2,..., μn are the Seidel eigenvalues of G‎. ‎The Estrada index of the Seidel matrix of G is defined as SEE(G)=‎∑ni=1 eμi‎. ‎In this paper‎, ‎we compute the Estrada index of the Seidel matrix of some known graphs‎. ‎Also‎, ‎some bounds for the Seidel energy of graphs are given‎.

Keywords

References

[1] T. Aleksić, I. Gutman and M. Petrović, Estrada index of iterated line graphs, Bull. Cl. Sci. Math. Nat. Sci. Math. 134 (2007) 33 − 41.
[2] J. Askari, A. Iranmanesh and K. C. Das, Seidel-Estrada index, J. Inequal. Appl. (2016) 120, 9 pp.
[3] N. Biggs, Algebraic Graph Theory, Cambridge University Press, Cambridge, 1993.
[4] A. E. Brouwer and W. H. Haemers, Spectra of Graphs, Universitext, Springer, New York, 2012.
[5] J. A. De la Pe˜ na, I. Gutman and J. Rada, Estimating the Estrada index, Linear Algebra Appl. 427 (2007) 70 − 76.
[6] E. Estrada, Characterization of 3D molecular structure, Chem. Phys. Lett. 319 (2000) 713 – 718.
[7] E. Estrada, Characterization of the folding degree of proteins, Bioinformatics 18 (2002) 697 − 704.
[8] E. Estrada and J. A. Rodríguez-Velázquez, Subgraph centrality in complex networks, Phys. Rev. E 71 (5) (2005) 056103, 9 pp.
[9] E. Estrada, Topological structural classes of complex networks, Phys. Rev. E 75 (2007) 016103.
[10] M. Ghorbani, On the energy and Estrada index of Cayley graphs, Discrete Math. Algorithms Appl. 7 (1) (2015) 1550005, 8 pp.
[11] M. Ghorbani and E. Bani-Asadi, On the Estrada and Laplacian Estrada In-dices of Fullerenes, J. Comput. Theor. Nanosci. 12 (6) (2015) 1064 − 1068.
[12] G. Greaves, J. H. Koolen, A. Munemasa and F. Szöllősi, Equiangular lines in Euclidean spaces, J. Combin. Theory Ser. A 138 (2016) 208 − 235.
[13] W. H. Haemers and G. R. Omidi, Universal adjacency matrices with two eigenvalues, Linear Algebra Appl. 435 (10) (2011) 2520 − 2529.
[14] W. H. Haemers, Seidel switching and graph energy, MATCH Commun. Math. Comput. Chem. 68 (3) (2012) 653 − 659.
[15] M. Hakimi-Nezhaad, H. Hua, A. R Ashrafi and S. Qian, The normalized Laplacian Estrada index of graphs, J. Appl. Math. Inform. 32 (1-2) (2014) 227 − 245.
[16] G. H. Hardy, J. E. Littlewood and G. Pólya, Inequalities, Cambridge Univer-sity Press, Cambridge, 1988.
[17] H. S. Ramane, M. M. Gundloor and S. M. Hosamani, Seidel equienergetic graphs, Bull. Math. Sci. Appl. 16 (2016) 62 − 69.
[18] R. Todeschini and V. Consonni, Handbook of Molecular Descriptors, Wiley-VCH, Weinheim, 2000.
[19] J. H. van Lint and J. J. Seidel, Equilateral point sets in elliptic geometry, Proc. KNAW A 69; Indag. Math. 28 (1966) 335 − 348.

Files

Share

How to cite

Statistics