| تعداد نشریات | 6 |
| تعداد شمارهها | 122 |
| تعداد مقالات | 1,550 |
| تعداد مشاهده مقاله | 1,642,765 |
| تعداد دریافت فایل اصل مقاله | 1,539,849 |
On Eccentric Euler Sombor Index of a Graph | ||
| Communications in Combinatorics and Optimization | ||
| مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 28 خرداد 1405 اصل مقاله (536.34 K) | ||
| نوع مقاله: Original paper | ||
| شناسه دیجیتال (DOI): 10.22049/cco.2026.30975.2686 | ||
| نویسندگان | ||
| Mohammad Habibi1؛ Izudin Redžepović* 2؛ Soheir Rouhani1، 3 | ||
| 1Department of Mathematics, Tafresh University, Tafresh 39518-79611, I. R. Iran | ||
| 2Department of Natural Sciences and Mathematics, State University of Novi Pazar, Serbia | ||
| 3Department of Mathematics and Computer Science, Amirkabir University of Technology, Tehran, Iran | ||
| چکیده | ||
| A novel vertex-degree-based topological index, namely the Euler Sombor index was defined as $ EU(G)=\sum\nolimits_{uv\in E(G)}{\sqrt{d_{u}^{2}+d_{v}^{2}+d_{u}d_{v}}}$. Based on this index, here we initiate the distance-based graph index as $\mathcal{E}_{ES}(G)=\sum\nolimits_{uv\in E(G)}{\sqrt{e^2(u)+e^2(v)+e(u)e(v)}}$ and call it the eccentric Euler Sombor index of a (chemical) graph $G = (V(G),E(G))$, where $e(u)$ and $e(v)$ are the eccentricity of $u$ and $v$ in $V(G)$, respectively. We establish basic mathematical properties of this new index. Also, we state some bounds for $\mathcal{E}_{ES}(G)$ in terms of order, size, degrees, radius, and diameter of $G$. We also determine trees (connected graphs, respectively) of a given order that have the minimum and maximum value of this index. Furthermore, we pose a conjecture about the maximum value of $\mathcal{E}_{ES}(G)$ when $G$ is a connected graph of fixed order. | ||
| کلیدواژهها | ||
| eccentric Euler Sombor index؛ tree؛ graph invariants؛ eccentricity؛ distance | ||
| مراجع | ||
|
[1] J.A. Bondy and U.S.R. Murty, Graph Theory, Springer Publishing Company, Incorporated, 2008.
[2] G. Chartrand, L. Lesniak, and P. Zhang, Graphs and Digraphs, Chapman and Hall/crc, 2015.
[3] K.C. Das, D.W. Lee, and A. Graovac, Some properties of the Zagreb eccentricity indices, Ars Math. Contemp. 6 (2013), no. 1, 117–125. https://doi.org/10.26493/1855-3974.237.48a
[4] N. De, New bounds for Zagreb eccentricity indices, Open J. Discrete Math. 3 (2013), no. 1, 70–74. http://dx.doi.org/10.4236/ojdm.2013.31014
[5] I. Gutman, Distance of thorny graphs, Publ. Inst. Math. 63 (1998), no. 83, 31–36.
[6] , Sombor index–one year later, Bulletin (Académie serbe des sciences et des arts. Classe des sciences math ematiques et naturelles. Sciences math´ematiques) (2020), no. 45, 43–55.
[7] , Geometric approach to degree-based topological indices: Sombor indices, MATCH Commun. Math. Comput. Chem. 86 (2021), no. 1, 11–16.
[8] , Relating Sombor and Euler indices, Vojnotehniˇcki glasnik 72 (2024), no. 1, 1–12. https://doi.org/10.5937/vojtehg72-48818
[9] I. Gutman, B. Furtula, and M.S. Öz, Geometric approach to vertex-degree-based topological indices–Elliptic Sombor index, theory and application, Int. J. Quantum Chem. 124 (2024), no. 2, e27346. https://doi.org/10.1002/qua.27346
[10] I. Gutman, I. Redžepović, G.Ö. Kizilirmak, and V.R. Kulli, Euler Sombor index and its congeners, Open J. Math. Sci. 9 (2025), 141–148. https://doi.org/10.30538/oms2025.0249
[11] I. Gutman and N. Trinajstić, Graph theory and molecular orbitals, total $\pi$-electron energy of alternant hydrocarbons, Chem. Phys. Lett. 17 (2025), 535–538. https://doi.org/10.1016/0009-2614(72)85099-1
[12] N. Harish, B. Sarveshkumar, and B. Chaluvaraju, The reformulated Sombor index of a graph, Trans. Comb. 13 (2024), no. 1, 1–16. https://doi.org/10.22108/TOC.2022.134155.1994
[13] O. Ivanciuc, Chemical graphs, molecular matrices and topological indices in chemoinformatics and quantitative structure-activity relationships, Curr. Comput. Aided Drug Des. 9 (2013), no. 2, 153–163. https://doi.org/10.2174/1573409911309020002
[14] M. Karelson, Molecular descriptors in QSAR/QSPR, Wiley-Interscience, New York, 2000.
[15] G.Ö. Kızılırmak, On Euler Sombor index of tricyclic graphs, MATCH Commun. Math. Comput. Chem. 94 (2025), no. 1, 247–262. https://doi.org/10.46793/match.94-1.247K
[16] V.R. Kulli, Different versions of Sombor index of some chemical structures, Int. J. Eng. Sci. Res. Technol. 10 (2021), no. 6-12, 23–32. https://doi.org/10.29121/ijesrt.v10.i7.2021.4
[17] Z. Lin, Sombor-type indices for certain interconnection networks, MATCH Commun. Math. Comput. Chem. 94 (2025), no. 3, 701–724. https://doi.org/10.46793/match.94-3.02525
[18] 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
[19] F. Qi and Z. Lin, Maximal elliptic Sombor index of bicyclic graphs, Contrib. Math. 10 (2024), 25–29. https://doi.org/10.47443/cm.2024.030
[20] H.S. Ramane, I. Gutman, K. Bhajantri, and D.V. Kitturmath, Sombor index of some graph transformations, Commun. Comb. Optim. 8 (2023), no. 1, 193–205. https://doi.org/10.22049/cco.2021.27484.1272
[21] I. Redžepović, Chemical applicability of Sombor indices, J. Serb. Chem. Soc. 86 (2021), no. 5, 445–457. https://doi.org/10.2298/JSC201215006R
[22] X. Ren, G. Cao, F. Wang, and M. Zhou, The Euler–Sombor index of trees, MATCH Commun. Math. Comput. Chem. 94 (2025), no. 3, 739–760. https://doi.org/10.46793/match94-3.07125
[23] K. Roy, S. Kar, and R.N. Das, A primer on QSAR/QSPR modeling: Fundamental concepts, Springer, 2015.
[24] S. Sahoo, C. Adhikari, M. Kuanar, and B.K. Mishra, A short review of the generation of molecular descriptors and their applications in quantitative structure property/activity relationships, Curr. Comput. Aided Drug Des. 12 (2016), no. 3, 181–205. [25] Y. Shang, Sombor index and degree-related properties of simplicial networks, Appl. Math. Comput. 419 (2022), 126881. https://doi.org/10.1016/j.amc.2021.126881
[26] V. Sharma, R. Goswami, and A.K. Madan, Eccentric connectivity index: A novel highly discriminating topological descriptor for structure-property and structure activity studies, J. Chem. Inf. Comput. Sci. 37 (1997), no. 2, 273–282. https://doi.org/10.1021/ci960049h [27] Z. Tang, Y. Li, and H. Deng, The Euler Sombor index of a graph, Int. J. Quantum Chem. 124 (2024), no. 9, e27387. https://doi.org/10.1002/qua.27387 [28] R. Todeschini and V. Consonni, Molecular Descriptors for Chemoinformatics, John Wiley and Sons, 2009.
[29] M. You and H. Deng, On higher-order Sombor index, Commun. Comb. Optim. 9 (2024), no. 3, 579–594. https://doi.org/10.22049/cco.2023.28658.1654 | ||
|
آمار تعداد مشاهده مقاله: 28 تعداد دریافت فایل اصل مقاله: 31 |
||