On the isomorphisms and automorphism groups of circulants
type: Item
instance of: scholarly article
title: On the isomorphisms and automorphism groups of circulants
zbMATH Open document ID: 0856.05047
DOI: 10.1007/BF01858452
published in: Graphs and Combinatorics
publication date: 1996-06-11T00:00:00Z
review text: Let \(M\) be a minimal generating set of the cyclic group \(Z_n\) and let \(\widetilde M = \{m, - m \mid m \in M\}\). Let \(M \subseteq S \subseteq \widetilde M\). The authors prove that if a circulant digraph of order \(n\) with symbol \(T\) is isomorphic to the circulant digraph of order \(n\) with symbol \(S\), then there exists an \(a \in Z^*_n\) such that \(T = aS\). They also determine the automorphism group of the circulant digraph with symbol \(S\).
Mathematics Subject Classification ID: 05C25
Mathematics Subject Classification ID: 05C60
Mathematics Subject Classification ID: 05C20
zbMATH DE Number: 887177
zbMATH Keywords: isomorphism
zbMATH Keywords: circulant digraph
zbMATH Keywords: automorphism group
author: Qiongxiang Huang
author: Jixiang Meng
reviewed by: Brian Alspach
MaRDI profile type: Publication
cites work: Point-symmetric graphs with a prime number of points
cites work: Isomorphism of circulant graphs and digraphs
cites work: A note on Adam's conjecture
cites work: Graphs with circulant adjacency matrices
cites work: Isomorphisms of circulant digraphs
cites work: The automorphism groups of Cayley digraphs of finite abelian groups with degree \(2\).
cites work: Q4770409
full work available at URL: https://doi.org/10.1007/bf01858452
OpenAlex ID: W2020496823
description: scientific article; zbMATH DE number 887177