Vertex transitive embeddings of complete graphs
type: Item
instance of: scholarly article
title: Vertex transitive embeddings of complete graphs
zbMATH Open document ID: 1187.05033
author: Cai Heng Li
published in: Journal of Combinatorial Theory. Series B
publication date: 2009-03-04T00:00:00Z
review text: A map is a cellular embedding of a finite \(1\)-complex (graph) into a compact, connected, closed surface. An automorphism of a map is a permutation of the vertices that preserves the cell structure of the map. A map \({\mathcal M}\) is called vertex transitive if the automorphism group \(\text{Aut}{\mathcal M}\) acts transitively on the vertex set. The purpose of this paper is to give a characterization of vertex transitive embeddings of complete graphs \(K_n.\) The author shows that there are four types of such maps \({\mathcal M}\) and illustrates their existence by examples. For instance, one of the four conditions states that \({\mathcal M}\) is a sharp Cayley map of \(\text{Aut}{\mathcal M}.\) An open problem asks for the number of non-isomorphic vertex transitive maps with underlying graph \(K_n.\)
Mathematics Subject Classification ID: 05C10
Mathematics Subject Classification ID: 05C25
zbMATH DE Number: 5523280
zbMATH Keywords: complete graphs
zbMATH Keywords: vertex transitive maps
zbMATH Keywords: Frobenius groups
zbMATH Keywords: Cayley maps
reviewed by: Hans Peter Künzi
MaRDI profile type: Publication
full work available at URL: j.jctb.2008.09.002
OpenAlex ID: W2063615235
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DOI: 10.1016/J.JCTB.2008.09.002
description: scientific article; zbMATH DE number 5523280