آمار
| تعداد نشریات | 5 |
| تعداد شماره‌ها | 117 |
| تعداد مقالات | 1,391 |
| تعداد مشاهده مقاله | 1,406,163 |
| تعداد دریافت فایل اصل مقاله | 1,373,479 |
On graphs with integer sombor indices | ||
| Communications in Combinatorics and Optimization | ||
| مقاله 6، دوره 9، شماره 4، اسفند 2024، صفحه 693-705 اصل مقاله (969.27 K) | ||
| نوع مقاله: Original paper | ||
| شناسه دیجیتال (DOI): 10.22049/cco.2023.28334.1510 | ||
| نویسندگان | ||
| Marzie Sepehr؛ Nader Jafari Rad* | ||
| Department of Mathematics, Shahed University, Tehran, Iran | ||
| چکیده | ||
| Sombor index of a graph $G$ is defined by $SO(G) = \sum_{uv \in E(G)} \sqrt{d^2_G(u)+d^2_G(v)}$, where $d_G(v)$ is the degree of the vertex $v$ of $G$. An $r$-degree graph is a graph whose degree sequence includes exactly $r$ distinctive numbers. In this article, we study $r$-degree connected graphs with integer Sombor index for $r \in \{5, 6, 7\}$. We show that: if $G$ is a 5-degree connected graph of order $n$ with integer Sombor index then $n \geq 50$ and the equality occurs if only if $G$ is a bipartite graph of size 420 with $SO(G) = 14830$; if $G$ is a 6-degree connected graph of order $n$ with integer Sombor index then $n \geq 75$ and the equality is established only for the bipartite graph of size $1080$; and if $G$ is a 7-degree connected graph of order $n$ with integer Sombor index then $n \geq 101$ and the equality is established only for the bipartite graph of size $1680$. | ||
| کلیدواژه‌ها | ||
| Integer Sombor index؛ Bipartite graphs؛ $r$-degree&lrm | ||
| مراجع | ||
|
[1] S. Alikhani and N. Ghanbari, Sombor index of polymers, MATCH Commun. Math. Comput. Chem. 86 (2021), no. 3, 715–728.
[2] R. Cruz, I. Gutman, and J. Rada, Sombor index of chemical graphs, Appl. Math. Comput. 399 (2021), Article ID: 126018. https://doi.org/10.1016/j.amc.2021.126018
[3] K.C. Das, A.S. C¸evik, I.N. Cangul, and Y. Shang, On Sombor index, Symmetry 13 (2021), no. 1, Article ID: 140. https://doi.org/10.3390/sym13010140
[4] K.C. Das and I. Gutman, On Sombor index of trees, Appl. Math. Comput. 412 (2022), Artice ID: 126575. https://doi.org/10.1016/j.amc.2021.126575
[5] T. Došlic, T. Réti, and A. Ali, On the structure of graphs with integer Sombor indices, Discrete Math. Lett. 7 (2021), 1–4.
[6] J. Eric, Linearly independent integer roots over the scalar field Q, (2007), preprint.
[7] I. Gutman, Geometric approach to degree-based topological indices: Sombor indices, MATCH Commun. Math. Comput. Chem. 86 (2021), no. 1, 11–16.
[8] I. Gutman, Sombor indices-back to geometry, Open J. Discrete Appl. Math. 5 (2022), no. 2, 1–5. https://doi.org/10.30538/psrp-odam2022.0072
[9] I. Gutman, N.K. Gürsoy, A. Gürsoy, and A. Ülker, New bounds on Sombor index, Commun. Comb. Optim. 8 (2023), no. 2, 305–311. https://doi.org/10.22049/cco.2022.27600.1296
[10] S. Kosari, N. Dehgardi, and A. Khan, Lower bound on the KG-Sombor index, Commun. Comb. Optim. 8 (2023), no. 4, 751–757. https://doi.org/10.22049/cco.2023.28666.1662
[11] M.R. Oboudi, Non-semiregular bipartite graphs with integer Sombor index, Discrete Math. Lett. 8 (2022), 38–40. https://doi.org/10.47443/dml.2021.0107
[12] M.R. Oboudi, On graphs with integer Sombor index, J. Appl. Math. Comput. 69 (2023), no. 1, 941–952. https://doi.org/10.1007/s12190-022-01778-z
[13] 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
[14] T. Réti, T. Došlic, and A. Ali, On the Sombor index of graphs, Contrib. Math. 3 (2021), 11–18. https://doi.org/10.47443/cm.2021.0006
[15] X. Sun and J. Du, On Sombor index of trees with fixed domination number, Appl. Math. Comput. 421 (2022), Atricle ID: 126946. https://doi.org/10.1016/j.amc.2022.126946 | ||
|
آمار تعداد مشاهده مقاله: 458 تعداد دریافت فایل اصل مقاله: 2,314 |
||