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New bounds for Seidel energy of graphs | ||
| Communications in Combinatorics and Optimization | ||
| مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 02 اردیبهشت 1405 اصل مقاله (390.04 K) | ||
| نوع مقاله: Original paper | ||
| شناسه دیجیتال (DOI): 10.22049/cco.2026.30809.2627 | ||
| نویسندگان | ||
| Mohammad Reza Oboudi* 1؛ Akbar Jahanbani2؛ Reza Sharafdini3 | ||
| 1Department of Mathematics, College of Science, Shiraz University, Shiraz, Iran | ||
| 2Sama Technical and Vocational School, Dolatabad Branch, Isfahan, Iran | ||
| 3Department of Mathematics, Persian Gulf University, Bushehr 75169-13817, Iran | ||
| چکیده | ||
| Let $G$ be a graph and $S(G)$ be the Seidel matrix of $G$. Let $s_1\ge s_2\ge \dots\ge s_n$ be the eigenvalues of $S(G)$. The spread of matrix $S(G)$ defined as $s(G) := max_{i,j}|s_i-s_j| = s_1-s_n$. The Seidel energy of $G$, denoted by $SE(G)$, is defined to be the sum of the absolute value of all eigenvalues of the Seidel matrix of $G$. Willem Haemers conjectured that the Seidel energy of any graph with $n$ vertices is at least $2n-2$. Motivated by this conjecture, we prove that the conjecture is true if $s(G)\le n$. Moreover, we present some new bounds for the Seidel energy and also we study some properties of the Seidel eigenvalues of $G$. Our results improve some known results. | ||
| کلیدواژهها | ||
| Seidel energy of graphs؛ Haemers' s conjecture؛ Seidel eigenvalues | ||
| مراجع | ||
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[1] S. Akbari, J. Askari, and K.C. Das, Some properties of eigenvalues of the Seidel matrix, Linear Multilinear Algebra 70 (2022), no. 11, 2150–2161. https://doi.org/10.1080/03081087.2020.1790481
[2] 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. https://doi.org/10.1016/j.ejc.2019.103078
[3] D.S. Bernstein, Matrix mathematics: Theory, facts and formulas, Princeton University Press, Princeton, USA, 2009.
[4] S. Filipovski, Improved Cauchy-Schwarz inequality and its applications, Turkish J. Ineq. 3 (2019), no. 2, 8–12.
[5] E. Ghorbani, On eigenvalues of Seidel matrices and Haemers’ conjecture, Des. Codes Cryptogr. 84 (2017), no. 1, 189–195. https://doi.org/10.1007/s10623-016-0248-x
[6] G. Greaves, J.H. Koolen, A. Munemasa, and F. Sz¨oll˝osi, Equiangular lines in Euclidean spaces, J. Combin. Theory Ser. A 138 (2016), 208–235. https://doi.org/10.1016/j.jcta.2015.09.008
[7] W.H. Haemers, Seidel switching and graph energy, MATCH Commun. Math. Comput. Chem. 68 (2012), 653–659.
[8] A. Iranmanesh and J.A. Farsangi, Upper and lower bounds for the power of eigenvalues in Seidel matrix, J. Appl. Math. Informatics 33 (2015), no. (5-6), 627–633. https://doi.org/10.14317/jami.2015.627
[9] M.R. Kanna, R.P. Kumar, and M.R. Farahani, Milovanovic bounds for Seidel energy of a graph, Advances in Theoretical and Applied Mathematics 10 (2016), no. 1, 37–44.
[10] H. Kober, On the arithmetic and geometric means and the H¨older inequality, Proc. Am. Math. Soc. 59 (1958), 452–459.
[11] D.S. Mitrinović, J.E. Pecaric, and A.M. Fink, Classical and new inequalities in analysis, Kluwer Academic Publishers, Dordrecht, 2013.
[12] P. Nageswari and P.B. Sarasija, Seidel energy and its bounds, Int. J. Math. Anal. 8 (2014), no. 57, 2869–2871. http://dx.doi.org/10.12988/ijma.2014.410309
[13] M.R. Oboudi, Energy and seidel energy of graphs, MATCH Commun. Math. Comput. Chem. 75 (2016), no. 2, 291–303.
[14] M.R. Oboudi, Seidel energy of complete multipartite graphs, Spec. Matrices 9 (2021), no. 1, 212–216.
[15] M.R. Oboudi, On the seidel estrada index of graphs, Linear Multilinear Algebra 72 (2024), no. 10, 1625–1632. https://doi.org/10.1080/03081087.2023.2192459 [16] M.R. Oboudi and M.A. Nematollahi, Improving a lower bound for Seidel energy of graphs, MATCH Commun. Math. Comput. Chem. 89 (2023), no. 2, 489–502. https://doi.org/10.46793/match.89-2.489O
[17] J.H. Van Lint and J.J. Seidel, Equilateral point sets in elliptic geometry, Indag. Math. 28 (1966), 335–348. | ||
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