The spectral radius and energy for atom-bond sum-connectivity matrix

Jiangtong Liu; Xiangyu Ren; Jiangtong Liu; Xiangyu Ren

doi:10.3934/math.2026095

AIMS Mathematics

2026, Volume 11, Issue 1: 2343-2362. doi: 10.3934/math.2026095

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Research article

The spectral radius and energy for atom-bond sum-connectivity matrix

Jiangtong Liu ,
Xiangyu Ren ^,

School of Mathematics and Statistics, Shanxi University, Taiyuan 030006, Shanxi, China

Received: 19 November 2025 Revised: 28 December 2025 Accepted: 09 January 2026 Published: 26 January 2026
MSC : 05C15, 05C22, 05C31

This paper investigates the spectral radius and energy of the atom-bond sum-connectivity (ABS) matrix. Through rigorous mathematical analysis, we establish bounds for the ABS spectral radius across several graph classes and investigate its properties. The ABS energy is defined, and its calculation methods and properties are studied. Furthermore, by analyzing the correlation between the ABS spectral radius and the physicochemical properties of octane isomers, it is revealed that the ABS spectral radius performs well in predicting molecular properties, indicating its potential application value in chemical structure-property modeling.
- ABS index,
- ABS spectral radius,
- ABS energy,
- ABS matrix,
- correlation analysis
Citation: Jiangtong Liu, Xiangyu Ren. The spectral radius and energy for atom-bond sum-connectivity matrix[J]. AIMS Mathematics, 2026, 11(1): 2343-2362. doi: 10.3934/math.2026095

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Abstract

This paper investigates the spectral radius and energy of the atom-bond sum-connectivity (ABS) matrix. Through rigorous mathematical analysis, we establish bounds for the ABS spectral radius across several graph classes and investigate its properties. The ABS energy is defined, and its calculation methods and properties are studied. Furthermore, by analyzing the correlation between the ABS spectral radius and the physicochemical properties of octane isomers, it is revealed that the ABS spectral radius performs well in predicting molecular properties, indicating its potential application value in chemical structure-property modeling.

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