Extremal trees for the general Sombor index

Phanjoubam, Chinglensana; Mawiong, Sainkupar Mn; Buhphang, Ardeline M.

doi:10.22049/cco.2024.29444.1996

تعداد نشریات	6
تعداد شماره‌ها	125
تعداد مقالات	1,580
تعداد مشاهده مقاله	1,733,010
تعداد دریافت فایل اصل مقاله	1,611,543

	Extremal trees for the general Sombor index
Communications in Combinatorics and Optimization
مقاله 11، دوره 11، شماره 3، آذر 2026، صفحه 911-922 اصل مقاله (419.18 K)
نوع مقاله: Original paper
شناسه دیجیتال (DOI): 10.22049/cco.2024.29444.1996
نویسندگان
Chinglensana Phanjoubam¹؛ Sainkupar Mn Mawiong^* ²؛ Ardeline M. Buhphang¹
¹Department of Mathematics, North-Eastern Hill University, Shillong, India
²Department of Basic Sciences and Social Sciences, North-Eastern Hill University, Shillong, India
چکیده
Recently, the Sombor index of a graph has been extended to general Sombor index. The general Sombor index of a simple graph $G$ is defined as $SO_\alpha(G)=\displaystyle\sum_{uv\in E(G)}[d_G(u)^2+d_G(v)^2]^{{\alpha}/2}$, where $d_G(u)$ denotes the degree of a vertex $u$ in $G$ and $\alpha$ is a real number. In this paper, we obtain bounds for the general Sombor index of trees. We further determine the trees with the extremal general Sombor indices.
کلیدواژه‌ها
Sombor index؛ General Sombor index؛ Trees؛ Degree

مراجع
[1] B. Bollobás and P. Erdös, Graphs of extremal weights, Ars Combin. 50 (1998), 225–233. [2] R. Cruz, I. Gutman, and J. Rada, Sombor index of chemical graphs, Appl. Math. Comput. 399 (2021), Article ID: 126018. https://doi.org/10.1016/j.amc.2021.126018 [3] Q. Cui and L. Zhong, The general Randić index of trees with given number of pendent vertices, Appl. Math. Comput. 302 (2017), 111–121. https://doi.org/10.1016/j.amc.2017.01.021 [4] Q. Cui and L. Zhong, On the general sum-connectivity index of trees with given number of pendent vertices, Discrete Appl. Math. 222 (2017), 213–221. https://doi.org/10.1016/j.dam.2017.01.016 [5] K.C. Das, A.S. B. Zhou and N. Trinajstićevik, I.N. Cangul, and Y. Shang, On sombor index, Symmetry 13 (2021), no. 1, Article ID: 140. https://doi.org/10.3390/sym13010140 [6] Z. Du, B. Zhou, and N. Trinajstić, On the general sum-connectivity index of trees, Appl. Math. Lett. 24 (2011), no. 3, 402–405. https://doi.org/10.1016/j.aml.2010.10.038 [7] I. Gutman, Geometric approach to degree-based topological indices: Sombor indices, MATCH Commun. Math. Comput. Chem. 86 (2021), no. 1, 11–16. [8] Y. Hu, X. Li, and Y. Yuan, Trees with maximum general Randić index, MATCH Commun. Math. Comput. Chem. 52 (2004), 129–146. [9] Y. Hu, X. Li, and Y. Yuan, Trees with minimum general Randić index, MATCH Commun. Math. Comput. Chem. 52 (2004), 119–128. [10] X. Li, J. Liu, and L. Zhong, Trees with a given order and matching number that have maximum general Randi´ c index, Discrete Math. 310 (2010), no. 17-18, 2249–2257. https://doi.org/10.1016/j.disc.2010.04.028 [11] H. Liu, I. Gutman, L. You, and Y. Huang, Sombor index: review of extremal results and bounds, J. Math. Chem. 60 (2022), no. 5, 771–798. https://doi.org/10.1007/s10910-022-01333-y [12] H. Liu, X. Yan, and Z. Yan, Bounds on the general randić index of trees with a given maximum degree, MATCH Commun. Math. Comput. Chem. 58 (2007), no. 1, 155–166. [13] S. Nikolić, G. Kovačević, A. Miličević, and N. Trinajstić, The Zagreb indices 30 years after, Croat. Chem. Acta 76 (2003), no. 2, 113–124. [14] C. Phanjoubam and S.M. Mawiong, On Sombor index and some topological indices, Iranian J. Math. Chem. 12 (2021), no. 4, 209–215. https://doi.org/10.22052/ijmc.2021.243137.1588 [15] C. Phanjoubam, S.M. Mawiong, and A.M. Buhphang, On general Sombor index of graphs, Asian-Eur. J. Math. 16 (2023), no. 3, Article ID: 2350052. https://doi.org/10.1142/S1793557123500523 [16] M. Randić, Characterization of molecular branching, J. Am. Chem. Soc. 97 (1975), no. 23, 6609–6615. https://doi.org/10.1021/ja00856a001 [17] I. Redžepović, Chemical applicability of Sombor indices, J. Serb. Chem. Soc. 86 (2021), no. 5, 445–457. http://dx.doi.org/10.2298/JSC201215006R [18] I. Tomescu and M.K. Jamil, Maximum general sum-connectivity index for trees with given independence number, MATCH Commun. Math. Comput. Chem. 72 (2014), no. 3, 715–722. [19] Z. Wang, Y. Mao, Y. Li, and B. Furtula, On relations between sombor and other degree-based indices, J. Appl. Math. Comput. 68 (2022), no. 1, 1–17. https://doi.org/10.1007/s12190-021-01516-x. [20] H. Wiener, Structural determination of paraffin boiling points, J. Am. Chem. Soc. 69 (1947), no. 1, 17–20. https://doi.org/10.1021/ja01193a005 [21] L.Z. Zhang, M. Lu, and F. Tian, Maximum Randić index on trees with k-pendant vertices, J. Math. Chem. 41 (2007), no. 2, 161–171. https://doi.org/10.1007/s10910-006-9066-0 [22] L. Zhong, General Randić index on trees with a given order diameter, MATCH Commun. Math. Comput. Chem. 62 (2009), no. 1, 177–187. [23] L. Zhong and Q. Qian, The minimum general sum-connectivity index of trees with given matching number, Bull. Malays. Math. Sci. Soc. 43 (2020), no. 2, 15271544. https://doi.org/10.1007/s40840-019-00755-3 [24] B. Zhou and N. Trinajstić, On a novel connectivity index, J. Math. Chem. 46 (2009), no. 4, 1252–1270. https://doi.org/10.1007/s10910-008-9515-z [25] B. Zhou and N. Trinajstić, On general sum-connectivity index, J. Math. Chem. 47 (2010), no. 1, 210–218. https://doi.org/10.1007/s10910-009-9542-4
آمار تعداد مشاهده مقاله: 273 تعداد دریافت فایل اصل مقاله: 329

سامانه مدیریت نشریات علمی. قدرت گرفته از سیناوب

پیوندهای مفید

آمار

Extremal trees for the general Sombor index