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September 18, 2025Open Access

Extremal values of the Hyperbolic Sombor index of unicyclic and bicyclic graphs

Key Points

The study establishes the extremal values of the hyperbolic sombor index for unicyclic and bicyclic graphs.
It characterizes the corresponding extremal graphs that achieve these maximum and minimum index values.
The research highlights the mathematical significance of vertex-degree-based topological indices in graph theory.
These findings have potential applications in chemical graph theory and related fields.

Abstract

The Hyperbolic Sombor index (abbreviated as HSO) is a recently proposed vertex-degree-based topological index, defined as HSO (G) =∑uv∈E (G) d2 (u) +d2 (v) mind (u), d (v). While chemical applications and certain mathematical properties of this index have been studied previously, this paper establishes the maximum and minimum values of the Hyperbolic Sombor index over unicyclic and bicyclic graphs. Furthermore, we characterize all the corresponding extremal graphs attaining these bounds.

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Cite This Study

Luo et al. (Wed,) studied this question.

synapsesocial.com/papers/68d462db31b076d99fa627ef https://doi.org/https://doi.org/10.22541/au.175808354.48331931/v1

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