A characterization of locally finite vertex-transitive graphs
type: Item
instance of: scholarly article
title: A characterization of locally finite vertex-transitive graphs
zbMATH Open document ID: 0632.05048
DOI: 10.1016/0095-8956(87)90033-5
author: Carsten Thomassen
published in: Journal of Combinatorial Theory. Series B
publication date: 1987-01-01T00:00:00Z
review text: In 1985 the reviewer asked the following: Is it true if G is a connected, locally-finite graph with the property that all its vertex-deleted subgraphs are isomorphic, then G must be regular? If G is regular then it is easy to prove that its automorphism group must act transitively on its vertex set. It is also not hard to prove that the answer to the above question is yes when G is finite. The author here proves that a locally finite graph without isolated vertices is vertex transitive if and only if all its vertex-deleted subgraphs are isomorphic, thus completely answering the original question. His proof is short and elegant.
Mathematics Subject Classification ID: 05C99
Mathematics Subject Classification ID: 05C60
zbMATH DE Number: 4027519
zbMATH Keywords: vertex transitive graph
zbMATH Keywords: vertex-deleted subgraphs
MaRDI profile type: Publication
full work available at URL: 0095-8956(87)90033-5
OpenAlex ID: W2074294228
cites work: Q3041212
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description: scientific article; zbMATH DE number 4027519