An integral family of quasi-strongly regular Cayley graphs

2025/11/18 by Poddar, Sauvik, Biswas, Sucharita, Das, Angsuman
Mathematics · #05C50 #05E10 #20C15 #Combinatorics (math.CO) #FOS: Mathematics #Finite Group Theory Research #Graph theory and applications #Group Theory (math.GR) #Rings, Modules, and Algebras

paper · doi:10.48550/arxiv.2511.14496

openalex publication_date 2025/11/18 · openalex created_date 2025/11/20 · openalex updated_date 2026/07/28

Abstract

Quasi-strongly regular graphs form a significant generalization of strongly regular graphs. We study the eigenvalues of a family of such graphs, Γ_H(G), constructed from a finite group G and a subgroup H. Our main results include a sufficient condition for Γ_H(G) to be integral and an explicit computation of its entire spectrum when H is normal, revealing that the spectrum in this case depends only on |G| and the index [G:H].

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