On finite groups all of whose cubic Cayley graphs are integral

2014/09/17 by Xuanlong Ma, Ma, Xuanlong, Kaishun Wang +1
Engineering · Mathematics · #05C25 #05C50 #20C10 #Combinatorics (math.CO) #FOS: Mathematics #Finite Group Theory Research #Graph theory and applications #Group Theory (math.GR) #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.1409.4939

openalex publication_date 2014/09/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For any positive integer k, let G_k denote the set of finite groups G such that all Cayley graphs \rm Cay(G,S) are integral whenever |S|≤ k. Est\rm \acuteelyi and Kov\rm \acuteacs \citeEK14 classified G_k for each k≥ 4. In this paper, we characterize the finite groups each of whose cubic Cayley graphs is integral. Moreover, the class G₃ is characterized. As an application, the classification of G_k is obtained again, where k≥ 4.

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