A note on the Seidel and Seidel Laplacian matrices
Resumen
In this paper we investigate the spectrum of the Seidel and Seidel Laplacian matrix of a graph. We generalized the concept of Seidel Laplacian matrix which denoted by Seidel matrix and obtained some results related to them. This can be intuitively understood as a consequence of the relationship between the Seidel and Seidel Laplacian matrix in the graph by Zagreb index. In closing, we mention some alternatives to and generalization of the Seidel and Seidel Laplacian matrices. Also, we obtain relation between Seidel and Seidel Laplacian energy, related to all graphs with order n.
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S. Akbari, J. Askari, K. Ch. Das, Some properties of eigenvalues of the Seidel matrix, Linear and Multilinear Algebra, 1. 12, (2020). https://doi.org/10.1080/03081087.2020.1790481
J. Askari, A. Iranmanesh, K. Ch. Das, Seidel Estrada-Index, Journal of Inequalities and Applications (2016) 2016:120. https://doi.org/10.1186/s13660-016-1061-9
B. Borovicanin, K. Ch. Das, B. Furtula and I. Gutman, Bounds for Zagreb indices, MATCH Commun. Math. Comput. Chem., 78, (2017), 17-100.
A.E. Brouwer, W. H. Haemers, Spectra of Graphs, Springer, New York, 2012.
I. Gutman, N. Trinajst'c, Graph theory and molecular orbitals. III. Total π-electron energy of alternant hydrocarbons, Chem. Phys. Lett., 17, (1972), 535-538. https://doi.org/10.1016/0009-2614(72)85099-1
I. Gutman, The energy of a graph: Old and new results, in: A. Betten, A. Kohner, R. Laue, A. Wassermann (Eds.), Algebraic Combinatorics and Applications, Springer, Berlin, (2001), 196-211. https://doi.org/10.1007/978-3-642-59448-9_13
W. H. Haemers, Seidel switching and graph energy, MATCH Commun. Math. Comput. Chem., 68, (2012), 653-659. https://doi.org/10.2139/ssrn.2026916
A. Iranmanesh, J. Askari, Upper and lower bounds for the power of eigenvalues in Seidel matrix, J. Appl. Math. Informatics., 33, (2015), 627-633. https://doi.org/10.14317/jami.2015.627
H. Kober, On the arithmetic and geometric means and the Holder inequality, Proc. Am. Math. Soc., 59, (1958), 452-459. https://doi.org/10.1090/S0002-9939-1958-0093564-7
J. Koolen, V. Moulton, Maximal energy graphs, Adv. Appl. Math., 26, (2001), 47-52. https://doi.org/10.1006/aama.2000.0705
P. Nageswari, P. B. Sarasija, Seidel energy and its bounds, International Journal of Mathematical Analysis., 8, (2014), 2869-2871. https://doi.org/10.12988/ijma.2014.410309
H. S. Ramane, M. M. Gundloor, 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
H. S. Ramane, R. B. Jummannaver, I.Gutman, Seidel Laplacian energy of graphs, Int. J. Appl. Graph Theory., 1, (2017), 74-82.
J. H. van Lint, J. J. Seidel, Equilateral point sets in elliptic geometry, Indag. Math., 28, (1966), 335-348. https://doi.org/10.1016/S1385-7258(66)50038-5
B. Zhu, I. Gutman, T. Aleksic, A note on the Laplacian energy of graphs, MATCH Commun. Math. Comput. Chem., 60, (2008), 441-446.
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