آمار
| تعداد نشریات | 6 |
| تعداد شمارهها | 122 |
| تعداد مقالات | 1,559 |
| تعداد مشاهده مقاله | 1,666,880 |
| تعداد دریافت فایل اصل مقاله | 1,556,985 |
The elliptic Sombor energy of graphs | ||
| Communications in Combinatorics and Optimization | ||
| مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 19 مرداد 1404 اصل مقاله (439.93 K) | ||
| نوع مقاله: Original paper | ||
| شناسه دیجیتال (DOI): 10.22049/cco.2025.30210.2361 | ||
| نویسندگان | ||
| Dilbak Mohammad* 1؛ Delbrin Ahmed2؛ Muwafaq Salih2 | ||
| 1Department of Mathematics, College of Science, University of Duhok, Duhok, Kurdistan Region,Iraq | ||
| 2Department of Mathematics, College of Basic Education, University of Duhok, Duhok, Kurdistan Region,Iraq | ||
| چکیده | ||
| The elliptic Sombor index is a topological index based on vertex degree introduced by Gutman. Suppose $G=(V(G), E(G))$ is a finite, connected, and simple graph with $V(G)=\{w_1, w_2, \dots, w_p\}$. Suppose $d_{G}(w_i)$ is the degree of $w_i$, for $1\leq i \leq p$. We use $ES(G)$ to represent the Sombor elliptic matrix $G$ which is a $p\times p$ matrix and its $(i, j)$-entry is equal to $(d_{G}(w_{i})+d_{G}(w_{j}))\sqrt{d_{G}^{2}(w_{i})+d_{G}^{2}(w_{j})}$ if $w_{i}w_{j}\in E(G)$, and zero otherwise. We introduce and investigate the elliptic Sombor energy and elliptic Sombor Estrada index, both base on the eigenvalues of the elliptic Sombor matrix. In addition, we prove some bounds for these new graph invariants. | ||
| کلیدواژهها | ||
| Sombor index؛ energy of graphs؛ topoligical indices | ||
| مراجع | ||
|
[1] S. Alikhani, N. Ghanbari, and M.A. Dehghanizadeh, Elliptic Sombor energy of a graph, J. Disc. Math. Appl. 10 (2025), no. 2, 143–155. https://doi.org/10.22061/JDMA.2024.11190.1089
[2] V. Anandkumar and R.R. Iyer, On the hyper-Zagreb index of some operations on graphs, Int. J. Pure Appl. Math 112 (2017), no. 2, 239–252. https://doi.org/10.12732/ijpam.v112i2.2
[3] A.E. Brouwer and W.H. Haemers, Spectra of Graphs, Springer Science & Business Media, 2011.
[4] S. Chanda and R.R. Iyer, On the Sombor index of Sierpiński and Mycielskian graphs, Commun. Comb. Optim. 10 (2025), no. 1, 20–56. https://doi.org/10.22049/cco.2023.28681.1669
[5] M.T. Cronin, J. Leszcynski, and T. Puzyn, Recent Advances in QSAR Studies Methods and Applications, Challenges and Advancesin Computational Chemistry and Physics,, Springer Dordrecht, London, New York, 2010.
[6] Q. Cui and L. Zhong, The general Randić index of trees with given number of pendent vertices, Appl. Math. Comput. 302 (2017), 111–121. https://doi.org/10.1016/j.amc.2017.01.021
[7] K.C. Das, S. Das, and B. Zhou, Sum-connectivity index of a graph, Front. Math. China 11 (2016), no. 1, 47–54. https://doi.org/10.1007/s11464-015-0470-2
[8] C. Espinal, I. Gutman, and J. Rada, Elliptic Sombor index of chemical graphs, Commun. Comb. Optim. 10 (2025), no. 4, 989–999. https://doi.org/10.22049/cco.2024.29404.1977
[9] B. Furtula and I. Gutman, A forgotten topological index, J. Math. Chem. 53 (2015), no. 4, 1184–1190. https://doi.org/10.1007/s10910-015-0480-z
[10] K.J. Gowtham and S.N. Narasimha, On Sombor energy of graphs, Nanosyst.:Phys., Chem., Math. 12 (2021), no. 4, 411–417. https://doi.org/10.17586/2220-8054-2021-12-4-411-417
[11] I. Gutman, Geometric approach to degree-based topological indices: Sombor indices, MATCH Commun. Math. Comput. Chem. 86 (2021), no. 1, 11–16.
[12] I. Gutman, B. Furtula, and M. Sinan Oz, Geometric approach to vertex-degree-based topological indices-elliptic Sombor index, theory and application, Int. J. Quantum Chem. 12 (2024), no. 2, e27346. https://doi.org/10.1002/qua.27346
[13] I. Gutman and N. Trinajsti´c, Graph theory and molecular orbitals. Total $\pi$-electron energy of alternant hydrocarbons, Chem. Phys. Lett. 17 (1972), no. 4, 535–538. https://doi.org/10.1016/0009-2614(72)85099-1
[14] N. Jafari Rad, A. Jahanbani, and I. Gutman, Zagreb energy and Zagreb Estrada index of graphs, MATCH Commun. Math. Comput. Chem. 79 (2018), no. 2, 371–386.
[15] V.R. Kulli, Modeified Sombor index and its exponential of a graph, Int. J. Math. Comput. Res. 12 (2024), no. 1, 3949–3954. https://doi.org/10.47191/ijmcr/v12i1.04
[16] X. Li and H. Zhao, Trees with the first three smallest and largest generalized topological indices, MATCH Commun. Math. Comput. Chem. 50 (2004), 57–62.
[17] H. Liu, Multiplicative Sombor index of graphs, Discrete Math. Lett 9 (2022), 80–85. https://doi.org/10.47443/dml.2021.s213
[18] J. Rada, J.M. Rodríguez, and J.M. Sigarreta, Sombor index and elliptic Sombor index of benzenoid systems, Appl. Math. Comput. 475 (2024), 128756. https://doi.org/10.1016/j.amc.2024.128756 | ||
|
آمار تعداد مشاهده مقاله: 322 تعداد دریافت فایل اصل مقاله: 253 |
||