Pentavalent vertex-transitive diameter two graphs
type: Item
instance of: scholarly article
title: Pentavalent vertex-transitive diameter two graphs
zbMATH Open document ID: 1382.05030
author: Wei Jin
published in: Frontiers of Mathematics in China
publication date: 2018-01-10T00:00:00Z
review text: This paper considers the class of \(5\)-valent, vertex-transitive graphs of diameter \(2\). For a graph \(\Gamma\) in this class with automorphism group \(A\), we call \(\Gamma\) distance-transitive if \(u\in V\Gamma\) and the stabilizer of \(u\) in \(A\) acts transitively both on the set of vertices adjacent to \(u\) and on the set of vertices at distance \(2\) from \(u\). It is shown that the graphs in this class that are not distance-transitive are exactly the following: \(\overline{C_8},\;\overline{2C_4}\), the Cartesian products \(K_5\square K_2\) and \(K_3\square K_4\), and the lexicographic product \(C_5[K_2]\). The distance-transitive graphs of valence \(5\) had been previously determined by \textit{A. E. Brouwer} et al. [Distance-regular graphs. Berlin etc.: Springer-Verlag (1989; Zbl 0747.05073)].
reviewed by: Mark E. Watkins
Mathematics Subject Classification ID: 05C25
Mathematics Subject Classification ID: 05E18
Mathematics Subject Classification ID: 05C12
Mathematics Subject Classification ID: 20B25
zbMATH DE Number: 6823735
zbMATH Keywords: automorphism group
zbMATH Keywords: arc-transitive
zbMATH Keywords: distance-transitive
zbMATH Keywords: Cartesian product
zbMATH Keywords: lexicographic product
zbMATH Keywords: diameter
MaRDI profile type: Publication
full work available at URL: s11464-016-0617-9
OpenAlex ID: W2558267699
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DOI: 10.1007/S11464-016-0617-9
description: scientific article; zbMATH DE number 6823735