Original Research Article

Article volume = 2021 and issue = 2

Pages: 152–159

Article publication Date: November, 1, 2021

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Seidel Energy of K-Fold and Strong K-Fold Graphs

Harishchandra S. Ramane(a), B. Parvathalu(b), K. Ashoka(a)

(a)Department of Mathematics, Karnatak University, Dharwad - 580003, India.

(b)Department of Mathematics, Karnatak University’s Karnatak Arts College, Dharwad - 580001, India.

Abstract:

The Seidel energy of a graph is the sum of absolute values of the eigenvalues of its Seidel matrix. In this paper, an explicit expression for the Seidel energy of k-fold graphs and strong k-fold graphs is obtained. As a consequence, certain Seidel equienergetic graphs are characterized. Moreover, some new class of Seidel equienergetic graphs are presented.

Keywords:

Seidel energy, Double graph, k-fold graph, Strong double graph, Strong k-fold graph.

References:
  • [1] S. Akbari, J. Askari, K. C. Das, Some properties of eigenvalues of the Seidel matrix, Linear Multilinear Algebra, 0 (2020), 1–12. https://doi.org/10.1080/03081087.2020.1790481 1
  • [2] S. Akbari, M. Einollahzadeh, M. M. Karkhaneei, M. A. Nematollahi, Proof of a conjecture on the Seidel energy of graphs, European J. Combin., 86 (2020), 103078, 8 p. 1
  • [3] A. E. Brouwer, W. H. Haemers, Spectra of Graphs, Springer, New York, (2012). 1, 2.6
  • [4] D. Cvetkovi´c, P. Rowlinson, S. Simi´c, An Introduction to the Theory of Graph Spectra, Cambridge Univ. Press, Cambridge, (2009). 2
  • [5] I. Gutman, The energy of a graph, Ber. Math. Statist. Sekt. Forsch. Graz, 103 (1978), 1–22. 1
  • [6] W. H. Haemers, Seidel switching and graph energy, MATCH Commun. Math. Comput. Chem., 68 (2012), 653–659. 1
  • [7] F. Harary, Graph Theory, Addison–Wesley, Reading, (1969). 2.1
  • [8] Y. Hou, L. Xu, Equienergetic bipartite graphs, MATCH Commun. Math. Comput. Chem., 57 (2007), 363–370. 3
  • [9] M. C. Marino, N. Z. Salvi, Generalizing double graphs, Atti della Accademia Peloritana dei Pericolanti-Classe di Scienze Fisiche, Matematiche e Naturali, 85(2) (2007), 1–9. 2.2
  • [10] E. Munarini, C. P. Cippo, A. Scagliola, N. Z. Salvi, Double graphs, Discrete Math., 308(2-3) (2008), 242–254. 2, 2
  • [11] M. R. Oboudi, Energy and Seidel energy of graphs, MATCH Commun. Math. Comput. Chem., 75 (2016), 291–303. 1
  • [12] S. Pirzada, H. A. Ganie, Spectra, energy and Laplacian energy of strong double graphs, in: D. Mugnolo (Eds.), Mathematical Technology of Networks, Springer, Cham, (2015), pp. 175-189. 2
  • [13] H. S. Ramane, K. Ashoka, B. Parvathalu, D. Patil, On A-energy and S-energy of certain class of graphs, Acta Univ. Sapientiae Informatica, 2021 (2021), 25 pages. 3.5, 3, 3.10
  • [14] H. S. Ramane, D. Patil, K. Ashoka, B. Parvathalu, Equienergetic graphs using Cartesian product and generalized composition, Sarajevo J. Math., 17 (2021), 7–21. 3
  • [15] H. S. Ramane, B. Parvathalu, D. Patil, K. Ashoka, Iterated line graphs with only negative eigenvalues -2, their complements and energy, (2021), Manuscript communicated for publication. 2.7
  • [16] H. S. Ramane, I. Gutman, M. M. Gundloor, Seidel energy of iterated line graphs of regular graphs, Kragujevac J. Math., 39(1) (2015), 7–12. 1, 2.8, 3
  • [17] H. S. Ramane, H. B. Walikar, S. B. Rao, B. D. Acharya, P. R. Hampiholi, S. R. Jog, I. Gutman, Spectra and energies of iterated line graphs of regular graphs, Appl. Math. Lett., 18(6) (2005), 679–682. 3
  • [18] H. S. Ramane, I. Gutman, H. B. Walikar, S. B. Halkarni, Equienergetic complement graphs, Kragujevac J. Sci., 27 (2005), 67–74. 3
  • [19] S. K. Vaidya, K. M. Popat, Some new results on Seidel equienergetic graphs, Kyungpook Math. J., 59(2) (2019), 335–340. 1, 2.4, 2.5, 3, 3, 3, 3, 4
  • [20] J. H. van Lint, J. J. Seidel, Equilateral point sets in elliptic geometry, Nederl. Akad.Wetensch. Proc. Ser. A, 69 & Indag. Math., 28(3) (1966), 335–348. 1
Cite this article as:
  • Harishchandra S. Ramane, B. Parvathalu, K. Ashoka, Seidel Energy of K-Fold and Strong K-Fold Graphs, Communications in Combinatorics, Cryptography & Computer Science, 2021(2), PP.152–159, 2021
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