Isomorphism problem for relational structures with a cyclic automorphism
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.
scientific article; zbMATH DE number 3993635
scientific article