2-Arc-transitive regular covers of $K_{n,n}$ having the covering transformation group $Z_p^2$,
2-Arc-transitive regular covers of $K_{n,n}$ having the covering transformation group $Z_p^2$,
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$K_{n,n}$ 的 2-弧传递正则覆盖，具有覆盖变换组 $Z_p^2$，
DOI：
10.1007/s00493-016-3511-x
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发表时间：
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通讯作者：
G.Y. Yan
中科院分区：
文献类型：
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作者：
S.F.Du;W.Q. Xu;G.Y. Yan
本文研究了有限2-弧传递图的分类问题。文[12]对完全二部图Kn，n的所有正则覆盖进行了分类，其覆盖变换群是循环的，其纤维保持自同构群是2-弧传递的。本文对Kn，n的所有正则覆盖作了进一步的分类，其覆盖变换群是p ~ 2阶初等阿贝尔群，其纤维保持自同构群是2-弧传递的.结果发现了两个新的2-弧传递图的无限族，并进一步说明了当覆盖变换群是p k阶的初等阿贝尔群时，对任意整数k的覆盖进行分类似乎是不可行的.
This paper contributes to the classification of finite 2-arc-transitive graphs. In [12], all the regular covers of complete bipartite graphsKn,nwere classified, whose covering transformation group is cyclic and whose fibre-preserving automorphism group acts 2-arc-transitively. In this paper, a further classification is achieved for all the regular covers ofKn,n, whose covering transformation group is elementary abelian group of orderp2and whose fibre-preserving automorphism group acts 2-arc-transitively. As a result, two new infinite families of 2-arc-transitive graphs are found. Moveover, it will be explained that it seems to be infeasible to classify all such covers when the covering transformation group is an elementary abelian group of orderpkfor an arbitrary integerk.