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General Randić index of unicyclic graphs with given maximum degree | ||
| Communications in Combinatorics and Optimization | ||
| مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 27 اردیبهشت 1404 اصل مقاله (423.76 K) | ||
| نوع مقاله: Original paper | ||
| شناسه دیجیتال (DOI): 10.22049/cco.2025.30340.2425 | ||
| نویسندگان | ||
| Elize Swartz؛ Tomáš Vetrík* | ||
| Department of Mathematics and Applied Mathematics, University of the Free State, Bloemfontein, South Africa | ||
| چکیده | ||
| The general Randi'{c} index of a graph $G$ is defined as $R_{a} (G) = \sum_{uv \in E(G)} [d_G (u) d_G (v)]^{a}$, where $a \in \mathbb{R}$, $E(G)$ is the set of edges of $G$, and $d_G (u)$ and $d_G (v)$ are the degrees of vertices $u$ and $v$, respectively. Among unicyclic graphs with given number of vertices and maximum degree, we present the graph with the largest value of $R_{a}$ for $a < 0$, and graphs having the smallest values of $R_{a}$ for $a > 0$. | ||
| کلیدواژه‌ها | ||
| extremal graph؛ topological index؛ cycle | ||
| مراجع | ||
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[1] M.R. Alfuraidan, K.C. Das, T. VetrÍk, and S. Balachandran, General Randić index of unicyclic graphs with given diameter, Discrete Appl. Math. 306 (2022), 7–16. https://doi.org/10.1016/j.dam.2021.09.016
[2] A. Ali and T. Idrees, A note on polyomino chains with extremum general sum-connectivity index, Commun. Comb. Optim. 6 (2021), no. 1, 81–91. https://doi.org/10.22049/cco.2020.26866.1153
[3] A. Altassan and M. Imran, General Randić index of unicyclic graphs and its applications to drugs, Symmetry 16 (2024), no. 1, Article ID: 113. https://doi.org/10.3390/sym16010113
[4] B. Bollobás and P. Erdös, Graphs of extremal weights, Ars Combin. 50 (1998), 225–233.
[5] D. Chen, Study of unicyclic graph with maximal general Randić index $R_{\alpha}$ for $\alpha <0$, Intelligent Computing and Information Science (Berlin, Heidelberg) (R. Chen, ed.), Springer Berlin Heidelberg, 2011, pp. 136–141.
[6] R. Hasni, N.H. Md Husin, and Z. Du, Unicyclic graphs with maximum Randić indices, Commun. Comb. Optim. 8 (2023), no. 1, 161–172. https://doi.org/10.22049/cco.2021.27230.1216
[7] X. Li, Y. Shi, and T. Xu, Unicyclic graphs with maximum general Randić index for $\alpha<0$, MATCH Commun. Math. Comput. Chem. 56 (2006), no. 3, 557–570.
[8] X. Li, L. Wang, and Y. Zhang, Complete solution for unicyclic graphs with minimum general Randić index, MATCH Commun. Math. Comput. Chem. 55 (2006), no. 2, 391–408.
[9] E. Swartz and T. Vetrík, General sum-connectivity index and general Randić index of trees with given maximum degree, Discret. Math. Lett. 12 (2023), 181–188. https://doi.org/10.47443/dml.2023.140
[10] E. Swartz and T. Vetrík, General sum-connectivity index of unicyclic graphs with given maximum degree, Discrete Appl. Math. 366 (2025), 238–249. https://doi.org/10.1016/j.dam.2025.01.033
[11] T. Vetrík and M. Masre, General eccentric connectivity index of trees and unicyclic graphs, Discrete Appl. Math. 284 (2020), 301–315. https://doi.org/10.1016/j.dam.2020.03.051
[12] B. Wu and L. Zhang, Unicyclic graphs with minimum general Randić index, MATCH Commun. Math. Comput. Chem. 54 (2005), no. 2, 455–464. | ||
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