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On Sombor index of extremal graphs | ||
| Journal of Discrete Mathematics and Its Applications | ||
| دوره 9، شماره 4، اسفند 2024، صفحه 335-344 اصل مقاله (491.56 K) | ||
| نوع مقاله: Full Length Article | ||
| شناسه دیجیتال (DOI): 10.22061/jdma.2024.11328.1101 | ||
| نویسندگان | ||
| Soheir Rouhani؛ Mohammad Habibi* ؛ Mohammad Ali Mehrpouya | ||
| Department of Mathematics, Tafresh University, Tafresh, 39518-79611, I. R. Iran | ||
| تاریخ دریافت: 13 مهر 1403، تاریخ بازنگری: 17 مهر 1403، تاریخ پذیرش: 22 آبان 1403 | ||
| چکیده | ||
| Let $ G $ be a finite simple graph. The Sombor index of $ G $ is defined as $ \sum\nolimits_{uv\in E(G)} \sqrt{d_{u}^{2}+d_{v}^{2}} $ where $d_{u}$ and $d_{v}$ represent the degrees of vertices $ u$ and $v$ in $ G $, respectively. The sum of the absolute values of the adjacency eigenvalues defines the energy of a graph. This paper aims to enhance the current connections between the Sombor index and the energy of graphs. Additionally, we provide some upper bounds for the Sombor index of triangle-free, square-free, $K_r$-free and tripartite graphs in terms of order, size and minimum degree. | ||
| کلیدواژهها | ||
| $C_4$-free graph؛ energy؛ Sombor index؛ tripartite graph؛ triangle-free graph | ||
| مراجع | ||
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[1] A. Aashtab, S. Akbari, S. Madadinia, M. Noei, F. Salehi, On the graphs with minimum Sombor index, MATCH Commun. Math. Comput. Chem. 88 (2022) 553– 559.https://doi.org/10.46793/match.88-3.553a [2] S. Akbari, H. Alizadeh, M. Fakharan, M. Habibi, S. Rabizadeh, S. Rouhani, Some relations between rank, vertex cover number and energy of graph, MATCH Commun. Math. Comput. Chem. 589 (2023) 653–664.https://doi.org/10.46793/match.89-3.653a [3] S. Akbari, M. Habibi, S. Rabizadeh, Relations between energy and Sombor index, MATCH Commun. Math. Comput. Chem. 92 (2024) 425–435.https://doi.org/10.46793/match.92-2.425a [4] S. Akbari, M. Habibi, S. Rouhani, A Note on an Inequality Between Energy and Sombor Index of a Graph, MATCH Commun. Math. Comput. Chem. f 90 (2023) 765–771. https://doi.org/10.46793/match.90-3.765a [5] O. Arizmendi, J. F. Hidalgo, O. Juarez-Romero, Energy of a vertex, Linear Algebra Appl. 557 (2018) 464–495. https://doi.org/10.1016/j.laa.2018.08.014 [6] H. Chen, W. Li, J. Wang, Extremal values on the Sombor index of trees, MATCH Commun. Math. Comput. Chem. 87 (2022) 23–49.https://doi.org/10.46793/match.87-1.023c [7] 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 [8] S. Filipovski, Relations between the energy of graphs and other graph parameters, MATCH Commun. Math. Comput. Chem. f 87 (2022) 661–672.https://doi.org/10.46793/match.87-3.661f [9] I. Gutman, Geometric approach to degreebased topological indices: Sombor indices, MATCH Commun. Math. Comput. Chem. 86 (2021) 11–16.https://doi.org/10.1002/qua.27346 [10] I. Gutman, The energy of a graph, Ber. Math. Statist. Sekt. Forschungsz. Graz. 103 (1978) 1–22. [11] I. Gutman, N. K. Gursoy, A. G ¨ ursoy, A. ¨ Ulker, New bounds on Sombor index, Commun. Comb. ¨ Optim. 8 (2) (2023) 305–311.https://doi.org/10.22049/cco.2022.27600.1296 [12] I. Gutman, S. Zare Firoozabadi, J. A. de la Pena, J. Rada, On the energy of ˜ regular graphs, MATCH Commun. Math. Comput. Chem. 57 (2007) 43–442. https://match.pmf.kg.ac.rs/electronic versions/Match57/n2/match57n2 435-442.pdf [13] A. E. Hamza, A. Ali, On a conjecture regarding the exponential reduced Sombor index of chemical trees, Discrete Math. Lett. 9 (2022) 107–110. https://doi.org/10.47443/dml.2021.s217 [14] S. Hayat, A. Rehman, On Sombor index of graphs with a given number of cut-vertices, MATCH Commun. Math. Comput. Chem. 89 (2023) 437–450.https://doi.org/10.46793/match.89-2.437h [15] B. Horoldagva, C. Xu, On Sombor Index of Graphs, MATCH Commun. Math. Comput. Chem. 86 (2021) 703–713. https://doi.org/10.47443/cm.2021.0006 [16] X. Li, Y. Shi, I. Gutman, Graph Energy, Springer, New York, 2012.https://doi.org/10.1007/978-1- 4614-4220-2 [17] H. Liu, Multiplicative Sombor index of graphs, Discrete Math. Lett. 9 (2022) 80– 85.https://doi.org/10.47443/dml.2021.s213 [18] H. Liu, L. You, Z. Tang, J.B. Liu, On the reduced Sombor index and its applications, MATCH Commun. Math. Comput. Chem. 86 (2021) 729–753. https://match.pmf.kg.ac.rs/electronic versions/Match86/n3/match86n3 729-753.pdf [19] J. A. Mendez-Berm ´ adez, R. Aguilar-S ´ anchez, E. D. Molina, J. M. Rodr ´ aguez, Mean Sombor index, ´ Discrete Math. Lett. 9 (2022) 18–25.https://doi.org/10.47443/dml.2021.s204 [20] M. R. Oboudi, The Mean Value of Sombor Index of Graphs, MATCH Commun. Math. Comput. Chem. 89 (2023) 733-740.https://doi.org/10.46793/match.89-3.733o [21] Ch. Phanjoubam, S. Mn Mawiong,A. M. Buhphang, On Sombor coindex of graphs, Commun. Comb. Optim. 8 (2023) 513–529.https://doi.org/10.22049/cco.2022.27751.1343 [22] I. Reiman, Uber ein Problem von K. Zarankiewicz, Acta Math. Acad. Sci. Hungar. 9 (1958) 269–273. ¨ [23] M. Selim Reja, S. Abu. Nayeem, On Sombor index and graph energy, MATCH Commun. Math. Comput. Chem. 89 (2023) 451–466.https://doi.org/10.46793/match.89-2.451r [24] P. Turan, Egy gr ´ afelm ´ eleti sz ´ elso ´ ert ´ ekfeladatr ´ ol, On an extremal problem in graph theory, in Hun- ´ garian, Mat. Fiz. Lapok 48 (1941) 436–452.https://bibliotekanauki.pl/articles/725575.pdf [25] A. Ulker, A. G ¨ ursoy, N. K. G ¨ ursoy, I. Gutman, Relating graph energy and Sombor index, Discrete ¨ Math. Lett. 8 (2022) 6–9.https://doi.org/10.47443/dml.2021.0085 [26] A. Ulker, A. G ¨ ursoy, N. K. G ¨ ursoy, The energy and Sombor index of graphs, MATCH Commun. ¨ Math. Comput. Chem. 87 (2022) 51–58.https://doi.org/10.46793/match.87-1.051u [27] Z. Yan, X. Zheng, J. Li, Some degree-based topological indices and (normalized Laplacian) energy of graphs, Discrete Math. Lett. 11 (2023) 19–26.https://doi.org/10.47443/dml.2022.059 | ||
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