A structure theory for regular graphs with fixed smallest eigenvalue

2024/01/19 by Yang Qianqian, Yang, Qianqian, Jack H. Koolen +1 · 1 citation
Computer Science · Mathematics · #05C50 #05C75 #Advanced Graph Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Finite Group Theory Research #Graph theory and applications

paper · pdf · doi:10.48550/arxiv.2401.10468

openalex publication_date 2024/01/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we will give a structure theory for regular graphs with fixed smallest eigenvalue. As a consequence of this theory, we show that a k-regular graph with smallest eigenvalue -λ has clique number linear in k if k is large with respect to λ.

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