Normal Cayley digraphs of cyclic groups with CI-property

2021/02/08 by Jin-Hua Xie, Xie, Jin-Hua, Yan‐Quan Feng +5
Computer Science · Engineering · Mathematics · #05C25 #20B25 #Coding theory and cryptography #Combinatorics (math.CO) #FOS: Mathematics #Finite Group Theory Research #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.2102.03976

openalex publication_date 2021/02/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A Cayley (di)graph Cay(G,S) of a group G with respect to a subset S of G is called normal if the right regular representation of G is a normal subgroup in the full automorphism group of Cay(G,S), and is called a CI-(di)graph if for every T⊆ G, Cay(G,S)≅ Cay(G,T) implies that there is σ∈ Aut(G) such that S^σ=T. We call a group G a NDCI-group if all normal Cayley digraphs of G are CI-digraphs, and a NCI-group if all normal Cayley graphs of G are CI-graphs, respectively. In this paper, we prove that a cyclic group of order n is a NDCI-group if and only if 8\nmid n, and is a NCI-group if and only if either n=8 or 8\nmid n.

Citations

• The Cayley isomorphism property for ℤ_p³ × ℤ_q
• On \BCI-groups and \CI-groups

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• Normal and non-normal Cayley digraphs on cyclic and dihedral groups
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• Dihedral groups with the m-DCI property
• The NNN-Property of Cyclic Groups