Extended Sombor Indices

Articles in Press

Document Type : Original paper

Authors

Department of Mathematics, School of Natural Sciences, National University of Sciences and Technology, H-12, Islamabad 44000, Pakistan

Abstract

In this paper, we present a novel perspective on vertex-degree-based topological indices. Established degree--based topological indices are based on adjacent vertices. One could contemplate including all pairs of vertices. Recently, Gutman introduced the Sombor indices. Here, we introduce the extended versions of the Sombor indices including all pairs of vertices in the Sombor indices formula. We explore the fundamental mathematical properties of these extended indices, establish upper and lower bounds in terms of some graph parameters, and find the sharp bounds. Additionally, we determine the extremal chemical trees with maximum and minimum extended Sombor index. Moreover, the role of extended Sombor indices in describing structure–property relationships is demonstrated.

Keywords

Main Subjects

References

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Communications in Combinatorics and Optimization

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Available Online from 17 July 2025

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