Augmented Sombor Index of Graph Operations

Articles in Press

Document Type : Original paper

Authors

1 Department of Mathematics Education, Farhangian University, Tehran, Iran

2 Department of Mathematics and Computer Science, Faculty of Basic Sciences, University of Bonab, Bonab, I.R. Iran

3 Education Department of District 5, Tabriz, Iran

Abstract

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.

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References

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Communications in Combinatorics and Optimization

Articles in Press, Accepted Manuscript
Available Online from 25 July 2026

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