آمار
| تعداد نشریات | 6 |
| تعداد شمارهها | 131 |
| تعداد مقالات | 1,634 |
| تعداد مشاهده مقاله | 1,898,037 |
| تعداد دریافت فایل اصل مقاله | 1,758,028 |
On the ordering of the Randić index of unicyclic and bicyclic graphs | ||
| Communications in Combinatorics and Optimization | ||
| مقاله 5، دوره 10، شماره 3، آذر 2025، صفحه 547-561 اصل مقاله (556.79 K) | ||
| نوع مقاله: Original paper | ||
| شناسه دیجیتال (DOI): 10.22049/cco.2023.28665.1661 | ||
| نویسندگان | ||
| Venkatesan Maitreyi1؛ Suresh Elumalai* 1؛ Bala Chandran Selvraj2 | ||
| 1Department of Mathematics, College of Engineering and Technology, Faculty of Engineering and Technology, SRM Institute of Science and Technology, Kattankulathur, Chengalpet 603 203, India | ||
| 2Department of Mathematics, School of Arts, Sciences and Humanities, SASTRA Deemed University, Thanjavur, India | ||
| چکیده | ||
| Let $d_x$ be the degree of the vertex $x$ in a graph $G$. The Randić index of $G$ is defined by $R(G) = \sum_{xy \in E(G)} (d_x d_y)^ {-\frac{1}{2}}$. Recently, Hasni et al. [Unicyclic graphs with Maximum Randi'{c} indices, Communication in Combinatorics and Optimization, 1 (2023), 161--172] obtained the ninth to thirteenth maximum Randić indices among the unicyclic graphs with $n$ vertices. In this paper, we correct the ordering of Randić index of unicyclic graphs. In addition, we present the ordering of maximum Randi'c index among bicyclic graphs of order $n$. | ||
| کلیدواژهها | ||
| unicyclic graphs؛ bicyclic graphs؛ Randić index | ||
| مراجع | ||
|
[1] A.M. Albalahi, A. Ali, Z. Du, A.A. Bhatti, T. Alraqad, N. Iqbal, and A.E. Hamza, On bond incident degree indices of chemical graphs, Mathematics 11 (2023), no. 1, Article ID: 27. https://doi.org/10.3390/math11010027
[2] A. Ali and D. Dimitrov, On the extremal graphs with respect to bond incident degree indices, Discrete Appl. Math. 238 (2018), 32–40. https://doi.org/10.1016/j.dam.2017.12.007
[3] B. Bollobás and P. Erdös, Graphs of extremal weights, Ars Combin. 50 (1998), 225–233.
[4] B. Bollobás, P. Erdös, and A. Sarkar, Extremal graphs for weights, Discrete Math. 200 (1999), no. 1-3, 5–19. https://doi.org/10.1016/S0012-365X(98)00320-3
[5] G. Caporossi, I. Gutman, P. Hansen, and L. Pavlović, Graphs with maximum connectivity index, Comp. Bio. Chem. 27 (2003), no. 1, 85–90. https://doi.org/10.1016/S0097-8485(02)00016-5
[6] T. Dehghan-Zadeh, A.R. Ashrafi, and N. Habibi, Maximum and second maximum of Randić index in the class of tricyclic graphs, MATCH Commun. Math. Comput. Chem. 74 (2015), no. 1, 137–144.
[7] J. Devillers and A.T. Balaban, Topological indices and related descriptors in QSAR and QSPR, Gordon and Breach, Amsterdam, 1999.
[8] Z. Du and B. Zhou, On Randić indices of trees, unicyclic graphs, and bicyclic graphs, Int.J. Quantum Chem. 111 (2011), no. 12, 2760–2770. http://doi.org/10.1002/qua.22596
[9] S. Elumalai and T. Mansour, A short note on tetracyclic graphs with extremal values of Randić index, Asian-Eur. J. Math. 13 (2020), no. 6, Article ID: 2050105. https://doi.org/10.1142/S1793557120501053
[10] J. Gao and M. Lu, On the Randić index of unicyclic graphs, MATCH Commun Math. Comput. Chem. 53 (2005), no. 2, 377–384.
[11] I. Gutman, Degree-based topological indices, Croat. Chem. Acta 86 (2013), no. 4, 351–361. http://dx.doi.org/10.5562/cca2294
[12] L.H. Hall and L.B. Kier, Molecular connectivity in structure activity analysis, Wiley, New York, 1986.
[13] 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
[14] L. Kier, Molecular connectivity in chemistry and drug research, Academic Press, New York, 1976.
[15] J. Li, S. Balachandran, S.K. Ayyaswamy, and Y.B. Venkatakrishnan, The Randić indices of trees, unicyclic graphs and bicyclic graphs, Ars Combin. 127 (2016), 409–419.
[16] X. Li and I. Gutman, Mathematical aspects of Randić-type molecular structure descriptors, Univ. Kragujevac, Kragujevac, 2006.
[17] X. Li and Y. Shi, A survey on the Randić index, MATCH Commun. Math. Comput. Chem. 59 (2008), no. 1, 127–156.
[18] M. Randić, Characterization of molecular branching, J. Am. Chem. Soc. 97 (1975), no. 23, 6609–6615. https://doi.org/10.1021/ja00856a001
[19] M. Randić, M. Nović, and D. Plavšić, Solved and Unsolved Problems of Structural Chemistry, CRC Press, Boca Raton, 2016.
[20] R. Todeschini and V. Consonni, Handbook of Molecular Descriptors, Wiley -VCH, Weinheim, 2000.
[21] R. Todeschini and V. Consonni, Molecular descriptors for chemo informatics, Wiley - VCH, Weinheim, 2009.
[22] J. Wang, Y. Zhu, and G. Liu, On the Randić index of bicyclic graphs, Recent Results in the Theory of Randi´c Index, in: Mathematical Chemistry Monograph (I. Gutman and B. Furtula, eds.), Univ. Kargujevac, Kargujevac, 2008, pp. 119–132.
[23] H. Zhao and X. Li, Trees with small randić connectivity indices, MATCH Commun Math. Comput. Chem. 51 (2004), 167–178. | ||
|
آمار تعداد مشاهده مقاله: 732 تعداد دریافت فایل اصل مقاله: 2,013 |
||