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Research Article | Open Access

Proof of a conjecture on the ϵ-spectral radius of trees

Jianping Li1( ), Leshi Qiu1, Jianbin Zhang2
School of Mathematics and Statistics, Guangdong University of Technology, Guangzhou 510090, China
School of Mathematical Sciences, South China Normal University, Guangzhou 510631, China
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Abstract

The ϵ-spectral radius of a connected graph is the largest eigenvalue of its eccentricity matrix. In this paper, we identify the unique n-vertex tree with diameter 4 and matching number 5 that minimizes the ϵ-spectral radius, and thus resolve a conjecture proposed in [W. Wei, S. Li, L. Zhang, Characterizing the extremal graphs with respect to the eccentricity spectral radius, and beyond, Discrete Math. 345 (2022) 112686].

Keywords

eccentricity matrixspectral radiusmatching number
CLC number: 05C50

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AIMS Mathematics
Volume 8 Issue 2,
February 2023
Pages 4363-4371
DOI: 10.3934/math.2023217

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Cite this article:
Li J, Qiu L, Zhang J. Proof of a conjecture on the ϵ-spectral radius of trees. AIMS Mathematics, 2023, 8(2): 4363-4371. https://doi.org/10.3934/math.2023217

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Received: 06 October 2022
Revised: 13 November 2022
Accepted: 16 November 2022
Published: 15 February 2023
©2023 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)