Extremal unicyclic and bicyclic graphs of the Euler Sombor index

Zhenhua Su; Zikai Tang; Zhenhua Su; Zikai Tang

doi:10.3934/math.2025289

AIMS Mathematics

2025, Volume 10, Issue 3: 6338-6354. doi: 10.3934/math.2025289

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Extremal unicyclic and bicyclic graphs of the Euler Sombor index

Zhenhua Su ¹,
Zikai Tang ^{2
,
,}

1.
School of Mathematics and Computational Sciences, Huaihua University, Huaihua, Hunan 418008, China
2.
College of Mathematics and Statistics, Hunan Normal University, Changsha, Hunan 410081, China

Received: 25 November 2024 Revised: 27 February 2025 Accepted: 06 March 2025 Published: 21 March 2025
MSC : 05C05, 05C09, 05C92

Topological indices are widely used to analyze and predict the physicochemical properties of compounds, and have good application prospects. Recently, the Euler Sombor index was introduced, which is defined as
$ \begin{align} EP(G) = \sum\limits_{v_iv_j\in E(G)}\sqrt{d(v_i)^2+d(v_j)^2+d(v_i)d(v_j)}.& \end{align} $
As the latest index with geometry motivation, it has excellent discrimination and predictive ability for compounds, in addition to mathematical practicality. The unicyclic graphs and bicyclic graphs are composed of various chemical structures, and are of particular importance in the study of topological indices. In this paper, the maximal and minimal values of Euler Sombor index for all unicyclic and bicyclic graphs are determined, and the corresponding extremal graphs are characterized.
- extremal value,
- unicyclic graph,
- bicyclic graph,
- Euler Sombor index
Citation: Zhenhua Su, Zikai Tang. Extremal unicyclic and bicyclic graphs of the Euler Sombor index[J]. AIMS Mathematics, 2025, 10(3): 6338-6354. doi: 10.3934/math.2025289

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Abstract

Topological indices are widely used to analyze and predict the physicochemical properties of compounds, and have good application prospects. Recently, the Euler Sombor index was introduced, which is defined as

$ \begin{align} EP(G) = \sum\limits_{v_iv_j\in E(G)}\sqrt{d(v_i)^2+d(v_j)^2+d(v_i)d(v_j)}.& \end{align} $

As the latest index with geometry motivation, it has excellent discrimination and predictive ability for compounds, in addition to mathematical practicality. The unicyclic graphs and bicyclic graphs are composed of various chemical structures, and are of particular importance in the study of topological indices. In this paper, the maximal and minimal values of Euler Sombor index for all unicyclic and bicyclic graphs are determined, and the corresponding extremal graphs are characterized.

References

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