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ON EDGE-PRIMITIVE GRAPHS WITH SOLUBLE EDGE-STABILIZERS
- Part of
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- Journal:
- Journal of the Australian Mathematical Society / Volume 113 / Issue 2 / October 2022
- Published online by Cambridge University Press:
- 06 August 2021, pp. 160-187
- Print publication:
- October 2022
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- Article
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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.
2-ARC-TRANSITIVE REGULAR COVERS OF
$K_{n,n}-nK_{2}$ HAVING THE COVERING TRANSFORMATION GROUP 
$\mathbb{Z}_{p}^{3}$
- Part of
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- Journal:
- Journal of the Australian Mathematical Society / Volume 101 / Issue 2 / October 2016
- Published online by Cambridge University Press:
- 16 March 2016, pp. 145-170
- Print publication:
- October 2016
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- Article
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This paper contributes to the regular covers of a complete bipartite graph minus a matching, denoted
$K_{n,n}-nK_{2}$ , whose fiber-preserving automorphism group acts 2-arc-transitively. All such covers, when the covering transformation group 
$K$ is either cyclic or 
$\mathbb{Z}_{p}^{2}$ with 
$p$ a prime, have been determined in Xu and Du [‘2-arc-transitive cyclic covers of 
$K_{n,n}-nK_{2}$ ’, J. Algebraic Combin.39 (2014), 883–902] and Xu et al. [‘2-arc-transitive regular covers of 
$K_{n,n}-nK_{2}$ with the covering transformation group 
$\mathbb{Z}_{p}^{2}$ ’, Ars. Math. Contemp.10 (2016), 269–280]. Finally, this paper gives a classification of all such covers for 
$K\cong \mathbb{Z}_{p}^{3}$ with 
$p$ a prime.
