On the minimum number of distinct eigenvalues of triangle-free strongly regular graphs

2025/02/07 by Emily Egolf, Egolf, Emily, Veronika Furst +1
Computer Science · Mathematics · #05C22 #05C50 #05E30 (Primary) #15A18 (Secondary) #Combinatorics (math.CO) #FOS: Mathematics #Finite Group Theory Research #Graph theory and applications #Matrix Theory and Algorithms

paper · pdf · doi:10.48550/arxiv.2502.05031

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

Abstract

Among the seven known (non-degenerate) triangle-free strongly regular graphs, we prove that the Clebsch graph describes a matrix with exactly two distinct eigenvalues while five of the graphs do not. In showing that the minimum number of distinct eigenvalues of the Sims-Gewirtz graph is three, we answer a recently stated open question.

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