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Augmented Sombor Index of Graph Operations | ||
| Communications in Combinatorics and Optimization | ||
| مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 03 مرداد 1405 اصل مقاله (415.05 K) | ||
| نوع مقاله: Original paper | ||
| شناسه دیجیتال (DOI): 10.22049/cco.2026.31428.2847 | ||
| نویسندگان | ||
| Fatemeh Raei* 1؛ Maryam Atapour2؛ Roghaye Asadpour3 | ||
| 1Department of Mathematics Education, Farhangian University, Tehran, Iran | ||
| 2Department of Mathematics and Computer Science, Faculty of Basic Sciences, University of Bonab, Bonab, I.R. Iran | ||
| 3Education Department of District 5, Tabriz, Iran | ||
| چکیده | ||
| The augmented Sombor index (ASO) is a vertex-degree-based topological index defined as \( ASO(G) = \sum_{uv \in E(G)} \sqrt{(d_u^2 + d_v^2)/(d_u + d_v - 2)} \). In this paper, we derive explicit formulas for the ASO index of graphs resulting from various graph operations, including the Cartesian product, join, corona product, and wreath product. We establish rigorous bounds for the ASO index under these operations and provide Nordhaus-Gaddum type results. Our work extends the mathematical theory of this recently introduced index and provides computational tools for its application in chemical graph theory. | ||
| کلیدواژهها | ||
| topological index؛ graph operation؛ Cartesian product؛ corona product؛ wreath product | ||
| مراجع | ||
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[2] A.M. Albalahi, A.M. Alanazi, A.M. Alotaibi, A.E. Hamza, and A. Ali, Optimizing the Euler Sombor index of (molecular) tricyclic graphs, MATCH Commun. Math. Comput. Chem. 94 (2025), no. 2, 549–560. https://doi.org/10.46793/match.94-2.549A
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[11] F. Movahedi, I. Gutman, I. Redžepović, and B. Furtula, Diminished Sombor index, MATCH Commun. Math. Comput. Chem. 95 (2026), no. 1, 141–162. https://doi.org/10.46793/match.95-1.14125 | ||
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