On automorphisms of direct products of Cayley graphs on abelian groups
type: Item
instance of: scholarly article
title: On automorphisms of direct products of Cayley graphs on abelian groups
zbMATH Open document ID: 1467.05119
DOI: 10.37236/9940
published in: The Electronic Journal of Combinatorics
publication date: 2021-07-06T00:00:00Z
review text: Summary: Let \(X\) and \(Y\) be connected Cayley graphs on abelian groups, such that no two distinct vertices of \(X\) have exactly the same neighbours, and the same is true about \(Y\). We show that if the number of vertices of \(X\) is relatively prime to the number of vertices of \(Y\), then the direct product \(X \times Y\) has only the obvious automorphisms (namely, the ones that come from automorphisms of its factors \(X\) and \(Y)\). This was not previously known even in the special case where \(Y = K_2\) has only two vertices. The proof of this special case is short and elementary. The general case follows from the special case by standard arguments.
Mathematics Subject Classification ID: 05C25
Mathematics Subject Classification ID: 05C76
zbMATH DE Number: 7368134
zbMATH Keywords: canonical bipartite double cover of a graph
zbMATH Keywords: twin-free graph
author: David Witte Morris
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.37236/9940
OpenAlex ID: W3181497812
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description: scientific article; zbMATH DE number 7368134