@article{Sun2026, 
author = {Shaowei Sun and Yaping Min and Kinkar Chandra Das},
title = {Extremal graphs for the sum of two largest eigenvalues},
year = {2026},
journal = {AIMS Mathematics},
volume = {11},
number = {5},
pages = {15028-15036},
keywords = {eigenvalue sum, adjacency matrix, graph spectrum, path graph},
url = {https://www.sciopen.com/article/10.3934/math.2026618},
doi = {10.3934/math.2026618},
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)".}
}