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On max-min rodeg index of graphs | ||
| Communications in Combinatorics and Optimization | ||
| مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 30 بهمن 1404 اصل مقاله (409.8 K) | ||
| نوع مقاله: Original paper | ||
| شناسه دیجیتال (DOI): 10.22049/cco.2026.30730.2597 | ||
| نویسندگان | ||
| Biswaranjan Khanra؛ Shibsankar Das* | ||
| Department of Mathematics, Institute of Science, Banaras Hindu University, Varanasi-221005, Uttar Pradesh, India | ||
| چکیده | ||
| Among the defined $148$ discrete Adriatic indices, the max-min rodeg index is one. It is a good predictor for the enthalpy of vaporization and standard enthalpy of vaporization for octane isomers, as well as the log water activity coefficient for polychlorobiphenyls. For a graph $G$, here we concentrate on the max-min rodeg index, defined as \begin{equation*} Mm_{sde}(G)=\sum_{x\sim y}\sqrt{\frac{max\{d_x, d_y\}}{min\{d_x, d_y\}}}, \end{equation*} where $x\sim y$ and $d_x$ represents the adjacency of two vertices $x$ and $y$, and the degree of the vertex $x$, respectively. First, we present some bounds for the max-min rodeg index via standard inequalities. Then we provide upper bounds via some graph parameters for the max-min rodeg index of $G$. Also, we obtain a relation between the max-min degree index and the energy of $G$. Finally, we study the extremal value problem over chemical graphs concerning the max-min rodeg index. | ||
| کلیدواژهها | ||
| max-min rodeg index؛ Diaz-metcalf inequality؛ clique number؛ energy؛ chemical graph | ||
| مراجع | ||
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[1] A. Ali, S. Stankov, E. Milovanović, M. Matejić, and I. Milovanović, Bounds on the modified second Zagreb index, Discrete Appl. Math. 342 (2024), 385–390. https://doi.org/10.1016/j.dam.2023.10.011
[2] G. Arizmendi and O. Arizmendi, Energy of a graph and Randic index, Linear Algebra Appl. 609 (2021), 332–338. https://doi.org/10.1016/j.laa.2020.09.025 [3] O. Arizmendi, J.F. Hidalgo, and O. Juarez-Romero, Energy of a vertex, Linear Algebra Appl. 557 (2018), 464–495. https://doi.org/10.1016/j.laa.2018.08.014 [4] S. Das and B. Khanra, Max-min degree index of a graph and it’s mathematical relation with other topological indices, Commun. Comb. Optim. (2025), In press. https://doi.org/10.22049/cco.2025.30390.2450
[5] I. Gutman, Geometric approach to degree-based topological indices: Sombor indices, MATCH Commun. Math. Comput. Chem. 86 (2021), no. 1, 11–16.
[6] I. Gutman, S.Z. Firoozabadi, J.A. de la Pena, and J. Rada, On the energy of regular graphs, MATCH Commun. Math. Comput. Chem. 57 (2007), no. 2, 435–442.
[7] B. Khanra and S. Das, Euler sombor index of trees, unicyclic and chemical graphs, MATCH Commun. Math. Comput. Chem 94 (2025), no. 2, 525–548. https://doi.org/10.46793/match.94–2.525K
[8] B. Khanra and S. Das, Max–min degree index of trees, unicyclic, bicyclic and chemical graphs, Natl. Acad. Sci. Lett. (2025), In press. https://doi.org/10.1007/s40009-025-01896-9
[9] B. Khanra and S. Das, Extremal GQ index of trees, unicyclic and bicyclic graphs, MATCH Commun. Math. Comput. Chem. 1 (2026), no. 96, 383–407. https://doi.org/10.46793/match.96-1.06925
[10] I. ˇZ. Milovanović, A. Ali, and Z. Raza, On the modified misbalance rodeg index, Contrib. Math. 9 (2024), 33–37. https://doi.org/10.47443/cm.2024.005 [11] Dragoslav S Mitrinovic and Petar M Vasic, Analytic Inequalities, vol. 1, Springer, 1970.
[12] M. Randić, Characterization of molecular branching, J. Am. Chem. Soc. 97 (1975), no. 23, 6609–6615.
[13] J. Sedlar, D. Vukičević, Mu. Aouchiche, and P. Hansen, Variable neighborhood search for extremal graphs, 24. results about the clique number, Stud. Inform. Univ. 8 (2010), 281–316.
[14] V.S. Shegehalli and R. Kanabur, Arithmetic-geometric indices of path graph, J. Math. Comput. Sci. 6 (2015), no. 1, 19–24.
[15] P. Turán, An extremal problem in graph theory, Mat. Fiz. Lapok 48 (1941), 436–452.
[16] D. Vukičević, Bond additive modeling 2. Mathematical properties of max-min rodeg index, Croat. Chem. Acta 83 (2010), no. 3, 261–273.
[17] D. Vukičević and M. Gašperov, Bond additive modeling 1. Adriatic indices, Croat. Chem. Acta 83 (2010), no. 3, 243–260.
[18] D.W. Zhao, W. Du, J. Li, and Z. Xie, Graphs that minimizing max–min rodeg index, J. Appl. Math. Comput. 67 (2021), no. 1, 495–505. https://doi.org/10.1007/s12190-020-01455-z | ||
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