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Research Article | Open Access

Extremal graphs for the sum of two largest eigenvalues

Shaowei Sun1, Yaping Min1, Kinkar Chandra Das2( )
School of Science, Zhejiang University of Science and Technology, Hangzhou, Zhejiang 310023, China
Department of Mathematics, Sungkyunkwan University, Suwon 16419, Republic of Korea
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Abstract

In this paper, we characterize all connected graphs for which the sum of two largest eigenvalues is less than 4. As an application, we prove that the path graph minimizes this sum among all connected graphs of order n ≥ 467, thereby solving a conjecture posed by Kumar, Liu, Monterde, Pragada, and Tait in "Maximum spectral sum of graphs (arXiv: 2604.00512v2)".

Keywords

eigenvalue sumadjacency matrixgraph spectrumpath graph
CLC number: 05C50, 15A18

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AIMS Mathematics
Volume 11 Issue 5,
May 2026
Pages 15028-15036
DOI: 10.3934/math.2026618

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Sun S, Min Y, Das KC. Extremal graphs for the sum of two largest eigenvalues. AIMS Mathematics, 2026, 11(5): 15028-15036. https://doi.org/10.3934/math.2026618

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Received: 12 March 2026
Revised: 19 May 2026
Accepted: 26 May 2026
Published: 15 May 2026
©2026 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)