Kyungpook Mathematical Journal

Department of Mathematics, Kyungpook National University (경북대학교 자연과학대학 수학과)
권호 표지
DOI QR코드

DOI QR Code

On the Seidel Laplacian and Seidel Signless Laplacian Polynomials of Graphs

  • Ramane, Harishchandra S. (Department of Mathematics, Karnatak University) ;
  • Ashoka, K. (Department of Mathematics, Karnatak University) ;
  • Patil, Daneshwari (Department of Mathematics, Karnatak University) ;
  • Parvathalu, B. (Department of Mathematics, Karnatak University's Karnatak Arts College)
  • Received : 2020.07.08
  • Accepted : 2020.10.05
  • Published : 2021.03.31
Download PDF
⟨ Previous Next ⟩

Abstract

We express the Seidel Laplacian polynomial and Seidel signless Laplacian polynomial of a graph in terms of the Seidel polynomials of induced subgraphs. Further, we determine the Seidel Laplacian polynomial and Seidel signless Laplacian polynomial of the join of regular graphs.

Keywords

References

  1. S. Akbari, M. Einollahzadeh, M. M. Karkhaneei and M. A. Nematollahi, Proof of a conjecture on the Seidel energy of graphs, European J. Combin., 86(2020), 103078, 8 pp. https://doi.org/10.1016/j.ejc.2019.103078
  2. A. E. Brouwer and W. H. Haemers, Spectra of graphs, Springer, Berlin, 2012.
  3. D. Cvetkovic, M. Doob and H. Sachs, Spectra of graphs: theory and application, Academic Press, New York, 1980.
  4. E. Ghorbani, On eigenvalues of Seidel matrices and Haemers conjecture, Des. Codes Cryptogr., 84(1-2)(2017), 189-195. https://doi.org/10.1007/s10623-016-0248-x
  5. I. Gutman, The energy of a graph, Ber. Math. Stat. Sekt. Forschungsz. Graz, 103(1978), 1-22.
  6. W. H. Haemers, Seidel switching and graph energy, MATCH Commun. Math. Comput. Chem., 68(3)(2012), 653-659.
  7. P. Nageswari and P. B. Sarasija, Seidel energy and its bounds, Int. J. Math. Anal., 8(57)(2014), 2869-2871. https://doi.org/10.12988/ijma.2014.410309
  8. X. Li, Y. Shi and I. Gutman, Graph energy, Springer, New York, 2012.
  9. M. R. Oboudi, Energy and Seidel energy of graphs, MATCH Commun. Math. Comput. Chem., 75(2)(2016), 291-303.
  10. H. S. Ramane, S. B. Gudimani and S. S. Shinde, Signless Laplacian polynomial and characteristic polynomial of a graph, J. Discr. Math., (2013), Art. ID 105624, 4 pp.
  11. H. S. Ramane, M. M. Gundloor and S. M. Hosamani, Seidel equienergetic graphs, Bull. Math. Sci. Appl., 16(2016), 62-69. https://doi.org/10.18052/www.scipress.com/bmsa.16.62
  12. H. S. Ramane, I. Gutman and M. M. Gundloor, Seidel energy of iterated line graphs of regular graphs, Kragujevac J. Math., 39(1)(2015), 7-12. https://doi.org/10.5937/KgJMath1501007R
  13. H. S. Ramane, I. Gutman, J. B. Patil and R. B. Jummannaver, Seidel signless Laplacian energy of graphs, Math. Interdisc. Res., 2(2017), 181-191.
  14. H. S. Ramane, R. B. Jummannaver and I. Gutman, Seidel Laplacian energy of graphs, Int. J. Appl. Graph Theory, 1(2)(2017), 74-82.
  15. S. K. Vaidya and K. M. Popat, Some new results on Seidel equienergetic graphs, Kyungpook Math. J., 59(2)(2019), 335-340. https://doi.org/10.5666/KMJ.2019.59.2.335
  16. H. B. Walikar and H. S. Ramane, Laplacian polynomial and number of spanning trees in terms of characteristic polynomial of induced subgraphs, AKCE Int. J. Graphs Combin., 5(1)(2008), 47-55.