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Proof of a conjecture on Sombor index | ||
| Journal of Discrete Mathematics and Its Applications | ||
| دوره 10، شماره 2، شهریور 2025، صفحه 157-160 اصل مقاله (241.63 K) | ||
| نوع مقاله: Short Communication | ||
| شناسه دیجیتال (DOI): 10.22061/jdma.2025.11904.1126 | ||
| نویسندگان | ||
| Mohammad Habibi* 1؛ Randhir Singh2 | ||
| 1Department of Mathematics, Tafresh University, Tafresh 39518-79611, I. R. Iran | ||
| 2Department of Mathematics, Savitribai Phule Pune University, Pune-411007, India. | ||
| تاریخ دریافت: 08 فروردین 1404، تاریخ بازنگری: 09 فروردین 1404، تاریخ پذیرش: 12 اردیبهشت 1404 | ||
| چکیده | ||
| Let $G$ be a simple graph. In this paper we prove the stated conjecture in [Some notes on Sombor index of graphs, MATCH Commun. Math. Comput. Chem.93 (2025) 853-859] and state an upper bound for the Sombor index of $G$ in terms of its size and the smallest eigenvalue of its Sombor matrix. Also, characterize all graphs for which the specified bound is attained. | ||
| کلیدواژهها | ||
| Sombor index؛ Sombor matrix؛ eigenvalue | ||
| مراجع | ||
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[1] K. C. Das, A. S. C¸ evik, I. N. Cangul, Y. Shang, On Sombor index, Symmetry 13 (2021) #140. https://doi.org/10.3390/sym13010140 [2] I. Gutman, Spectrum and energy of Sombor matrix, Milit. Tech. Cour. 69 (2021) 551–561. https://doi.org/10.5937/vojtehg69-31995 [3] I. Gutman, Geometric approach to degree-based topological indices: Sombor indices, MATCH Commun. Math. Comput. Chem. 86 (2021) 11–16.https:// match.pmf.kg.ac.rs /electronic versions/ Match86/ n1/ match86n1 11-16.pdf [4] B. Horoldagva, C. Xu, On Sombor index of graphs, MATCH Commun. Math. Comput. Chem. 86 (2021) 703–713. https://doi.org/10.48550/arXiv.2305.04554 [5] H. Liu, I. Gutman, L. You, Y. Huang, Sombor index: Review of extremal results and bounds, J. Math. Chem. 66 (2022) 771–798.https://doi.org/10.1007/s10910-022-01333-y [6] M. Mohammadi, H. Barzegar, Bounds for Sombor index using topological and statistical indices, J. Disc. Math. Appl. 10(1) (2025) 61–85.https://doi.org/10.22061/jdma.2025.11494.1107 [7] S. Rabizadeh, M. Habibi, I. Gutman, Some notes on Sombor index of graphs, MATCH Commun. Math. Comput. Chem. 93 (2025) 853–859.https://match.pmf.kg.ac.rs/ electronic versions/Match93/n3/ match93n3 853-859.pdf [8] J. Rada, J. M. Rodr´ıguez, J. M. Sigarreta, General properties on Sombor indices, Discr. Appl. Math. 299 (2021) 87–97.https://doi.org/10.1016/j.dam.2021.04.014 [9] S. Rouhani, M. Habibi, M. A. Mehrpouya, On Sombor index of extremal graphs, J. Disc. Math. Appl. 9(4) (2024) 335–344.https://doi.org/ 10.22061/jdma.2024.11328.1101 | ||
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