Isomorphism problem for relational structures with a cyclic automorphism
type: Item
instance of: scholarly article
title: Isomorphism problem for relational structures with a cyclic automorphism
zbMATH Open document ID: 0614.05049
DOI: 10.1016/S0195-6698(87)80018-5
published in: European Journal of Combinatorics
publication date: 1987-01-01T00:00:00Z
review text: Let \(T\subseteq \{0,1,2,...,n-1\}\). Then \(\Gamma\) (n,T) is the graph on n vertices labelled by the integers modulo n, such that (i,j) is an edge if and only if i-j\(\in T\) (arithmetic being done modulo n). Clearly for \((k,n)=1\), \(\Gamma\) (n,kT)\(\cong \Gamma (n,T)\). Ádám conjectured that if \(\Gamma\) (n,T')\(\cong \Gamma (n,T)\) then \(T'=kT\) for some k relatively prime to n. The conjecture turns out to be true if and only if \(n=4\) or \((n,\phi (n))=1\). This result extends to more general structures.
Mathematics Subject Classification ID: 05C99
Mathematics Subject Classification ID: 05C25
zbMATH DE Number: 3993635
zbMATH Keywords: Adam's conjecture
zbMATH Keywords: CI-group
Wikidata QID: Q106072080
author: Péter P. Pálfy
MaRDI profile type: Publication
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full work available at URL: s0195-6698(87)80018-5
OpenAlex ID: W1980897883
description: scientific article; zbMATH DE number 3993635