On groups all of whose undirected Cayley graphs of bounded valency are\n integral

2014/03/29 by István Estélyi, I. Kovács, Estélyi, István +1 · 1 citation
Engineering · Mathematics · #05C50 #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.1403.7602

openalex publication_date 2014/03/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A finite group G is called Cayley integral if all undirected Cayley graphs\nover G are integral, i.e., all eigenvalues of the graphs are integers. The\nCayley integral groups have been determined by Kloster and Sander in the\nabelian case, and by Abdollahi and Jazaeri, and independently by Ahmady, Bell\nand Mohar in the non-abelian case. In this paper we generalize this class of\ngroups by introducing the class \G_k of finite groups G for which\nall graphs \Cay(G,S) are integral if |S| \≤ k. It will be proved\nthat \G_k consists of the Cayley integral groups if k \≥ 6; and\nthe classes \G₄ and \G₅ are equal, and consist of: (1)\nthe Cayley integral groups, (2) the generalized dicyclic groups\n\Dic(E_3ⁿ \× \ℤ₆), where n \≥ 1.\n

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