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ON EDGE-PRIMITIVE GRAPHS WITH SOLUBLE EDGE-STABILIZERS

Part of: Permutation groups Graph theory

Published online by Cambridge University Press:  06 August 2021

HUA HAN Open the ORCID record for HUA HAN [Opens in a new window] ,
HONG CI LIAO  and
ZAI PING LU Open the ORCID record for ZAI PING LU [Opens in a new window]
HUA HAN
Affiliation:
School of Science, Tianjin University of Technology, Tianjin 300384, PR China e-mail: hh1204@mail.nankai.edu.cn
HONG CI LIAO
Affiliation:
Center for Combinatorics, LPMC, Nankai University, Tianjin 300071, PR China e-mail: 827436562@qq.com
ZAI PING LU*
Affiliation:
Center for Combinatorics, LPMC, Nankai University, Tianjin 300071, PR China
*
e-mail: lu@nankai.edu.cn
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Abstract

A graph is edge-primitive if its automorphism group acts primitively on the edge set, and $2$-arc-transitive if its automorphism group acts transitively on the set of $2$-arcs. In this paper, we present a classification for those edge-primitive graphs that are $2$-arc-transitive and have soluble edge-stabilizers.

Keywords

edge-primitive graph2-arc-transitive graphalmost simple group2-transitive groupsoluble group

MSC classification

Primary: 05C25: Graphs and abstract algebra (groups, rings, fields, etc.)
Secondary: 20B25: Finite automorphism groups of algebraic, geometric, or combinatorial structures

Information

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 113 , Issue 2 , October 2022 , pp. 160 - 187
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Copyright
© 2021 Australian Mathematical Publishing Association Inc.

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Footnotes

Communicated by Michael Giudici

The third author was supported by the National Natural Science Foundation of China (11971248 and 11731002) and the Fundamental Research Funds for the Central Universities.Michael Giudici

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