Edge‐transitive cubic graphs of twice square‐free order

A graph is edge‐transitive if its automorphism group acts transitively on the edge set. This paper presents a complete classification for connected edge‐transitive cubic graphs of order 2 n $2n$, where n $n$ is even and square‐free. In particular, it is shown that such a graph is either symmetric or...

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Bibliographic Details
Published inJournal of graph theory Vol. 108; no. 1; pp. 173 - 204
Main Authors Liu, Gui Xian, Lu, Zai Ping
Format Journal Article
LanguageEnglish
Published Hoboken Wiley Subscription Services, Inc 01.01.2025
Subjects
Automorphisms
bi‐coset graph
coset graph
edge‐transitive graph
Graphs
Group theory
semisymmetric graph
symmetric graph
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ISSN0364-9024
1097-0118
DOI10.1002/jgt.23168

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Summary:A graph is edge‐transitive if its automorphism group acts transitively on the edge set. This paper presents a complete classification for connected edge‐transitive cubic graphs of order 2 n $2n$, where n $n$ is even and square‐free. In particular, it is shown that such a graph is either symmetric or isomorphic to one of the following graphs: a semisymmetric graph of order 420, a semisymmetric graph of order 29,260, and five families of semisymmetric graphs constructed from the simple group PSL 2 ( p ) ${{\bf{\text{PSL}}}_{2}(p)$.
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ISSN:0364-9024
1097-0118
DOI:10.1002/jgt.23168