AI Chat Paper
Note: Please note that the following content is generated by AMiner AI. SciOpen does not take any responsibility related to this content.
{{lang === 'zh_CN' ? '文章概述' : 'Summary'}}
{{lang === 'en_US' ? '中' : 'Eng'}}
Chat more with AI
Powered by AMiner. Clicking this button will take you away from SciOpen.
Home AIMS Mathematics Article
PDF (219.9 KB)
Cite
EndNote(RIS) BibTeX
Collect
Submit Manuscript AI Chat Paper
Show Outline
Outline
Show full outline
Hide outline
Outline
Show full outline
Hide outline
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
Show Author Information

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

References

【1】
【1】
 
 
Crossref Google Scholar
AIMS Mathematics
Volume 11 Issue 5,
May 2026
Pages 15028-15036
DOI: 10.3934/math.2026618

{{item.num}}

Comments on this article

Go to comment

< Back to all reports

Review Status: {{reviewData.commendedNum}} Commended , {{reviewData.revisionRequiredNum}} Revision Required , {{reviewData.notCommendedNum}} Not Commended Under Peer Review

Review Comment

Cite this Report
Close
Close
Cite this article:
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

203

Views

5

Downloads

0

Crossref

0

Web of Science

0

Scopus
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)