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Exponential second Zagreb index of chemical trees | ||
| Transactions on Combinatorics | ||
| مقاله 2، دوره 10، شماره 2، شهریور 2021، صفحه 97-106 اصل مقاله (222.89 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22108/toc.2020.125047.1764 | ||
| نویسندگان | ||
| Selvaraj Balachandran* ؛ Tomas Vetrik | ||
| Department of Mathematics and Applied Mathematics, University of the Free State, P. O. Box 339, Bloemfontein, 9300, South Africa | ||
| چکیده | ||
| Cruz, Monsalve and Rada [Extremal values of vertex-degree-based topological indices of chemical trees, Appl. Math. Comput. 380 (2020) 125281] posed an open problem to find the maximum value of the exponential second Zagreb index for chemical trees of given order. In this paper, we solve the open problem completely. | ||
| کلیدواژهها | ||
| Topological index؛ degree؛ extremal graph theory | ||
| مراجع | ||
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[1] M. Aghel, A. Erfanian and A. R. Ashrafi, On the first and second Zagreb indices of quasi unicyclic graphs, Trans. Comb., 8 no. 3 (2019) 29–38. [2] A. R. Ashrafi, T. Došlić and A. Hamzeh, Extremal graphs with respect to the Zagreb coindices, MATCH Commun. Math. Comput. Chem., 65 no. 1 (2011) 85–92. [3] M. Azari, Generalized Zagreb index of product graphs, Trans. Comb., 8 no. 4 (2019) 35–48.
[4] R. Cruz, J. Monsalve and J. Rada, Extremal values of vertex-degree-based topological indices of chemical trees, Appl. Math. Comput., 380 (2020) 125–281. [5] R. Cruz, J. Monsalve and J. Rada, On chemical trees that maximize atom-bond connectivity index, its exponential version, and minimize exponential geometricarithmetic index, MATCH Commun. Math. Comput. Chem., 84 (2020) 691–718. [6] K. C. Das and A. Ali, On a conjecture about the second Zagreb index, Discrete Math. Lett., 2 (2019) 38–43.
[7] M. Liang, B. Cheng and J. Liu, Solution to the minimum harmonic index of graphs with given minimum degree, Trans. Comb., 7 no. 2 (2018) 25–33. [8] J. Rada, Exponential vertex-degree-based topological indices and discrimination, MATCH Commun. Math. Comput. Chem., 82 no. 1 (2019) 29–41. [9] Ž. K. Vukićević and G. Popivoda, Chemical trees with extreme values of Zagreb indices and coindices, Iran. J. Math. Chem., 5 no. 1 (2014) 19–29. | ||
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