Sesqui-regular graphs with fixed smallest eigenvalue

2019/04/02 by Jack H. Koolen, Brhane Gebremichel, Koolen, Jack H. +5
Materials Science · Mathematics · #05C50 #05C62 #05C75 #Combinatorics (math.CO) #FOS: Mathematics #Finite Group Theory Research #Graph theory and applications #Synthesis and properties of polymers

paper · pdf · doi:10.48550/arxiv.1904.01274

openalex publication_date 2019/04/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let λ≥2 be an integer. For strongly regular graphs with parameters (v, k, a,c) and smallest eigenvalue -λ, Neumaier gave two bounds on c by using algebraic property of strongly regular graphs. In this paper, we will study a new class of regular graphs called sesqui-regular graphs, which contains strongly regular graphs as a subclass, and prove that for a sesqui-regular graph with parameters (v,k,c) and smallest eigenvalue at least -λ, if k is very large, then either c ≤ λ²(λ-1) or v-k-1 ≤ ((λ-1)²)/(4) + 1 holds.

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