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Sombor index of product of graphs | ||
| Communications in Combinatorics and Optimization | ||
| مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 11 بهمن 1403 اصل مقاله (365.9 K) | ||
| نوع مقاله: Original paper | ||
| شناسه دیجیتال (DOI): 10.22049/cco.2025.30209.2360 | ||
| نویسنده | ||
| Mohammad Reza Oboudi* | ||
| Department of Mathematics, College of Science, Shiraz University, Shiraz, Iran | ||
| چکیده | ||
| Recently a new vertex-degree based molecular structure descriptor was defined as Sombor index. For a simple graph $G$, the Sombor index of $G$, denoted by $SO(G)$, is defined as $\sum_{uv\in E(G)}\sqrt{d_u^2+d_v^2},$ where $d_v$ is the degree of $v$. In this paper we study the Sombor index of many kinds of product of graphs, such as join of graphs, Cartesian product of graphs, tensor product of graphs, and lexicographic product of graphs. We obtain some formulas for the Sombor index of these product of graphs. | ||
| کلیدواژه‌ها | ||
| sombor index؛ product of graphs؛ regular graphs | ||
| مراجع | ||
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[9] M.R. Oboudi, The mean value of Sombor index of graphs, MATCH Commun. Math. Comput. Chem 89 (2023), no. 3, 733–740.
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[11] M.R. Oboudi, Sombor index of a graph and of its subgraphs, MATCH Commun. Math. Comput. Chem 92 (2024), no. 3, 697–702.
[12] M.R. Oboudi and A. Jahanbani, Bounds on Sombor energy of graphs, Iran J. Sci. 48 (2024), no. 2, 437–442. https://doi.org/10.1007/s40995-024-01604-0
[13] S. Oğuz Ünal, Nirmala and Banhatti-Sombor index over tensor and Cartesian product of special class of semigroup graphs, J. Math. 2022 (2022), no. 1, Article ID: 5770509. https://doi.org/10.1155/2022/5770509
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[17] I. Sarkar, M. Nanjappa, and I. Gutman, Bounds of Sombor index for corona products on R-graphs, Commun. Comb. Optim. 9 (2024), no. 1, 101–117. https://doi.org/10.22049/cco.2022.27904.1391
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