Graphs with second largest eigenvalue less than 1/2

2022/11/07 by WU Xiaoxia, Wu, Xiaoxia, Jianguo Qian +3
Computer Science · Mathematics · #05C50 #Advanced Graph Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Finite Group Theory Research #Graph theory and applications

paper · pdf · doi:10.48550/arxiv.2211.03380

openalex publication_date 2022/11/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We characterize the simple connected graphs with the second largest eigenvalue less than 1/2, which consists of 13 classes of specific graphs. These 13 classes hint that c₂∈ [1/2, √(2+√(5))], where c₂ is the minimum real number c for which every real number greater than c is a limit point in the set of the second largest eigenvalues of the simple connected graphs. We leave it as a problem.

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