Cubic Edge-Transitive Bi-p-Metacirculants
Cubic Edge-Transitive Bi-p-Metacirculants
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DOI：
10.37236/6417
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发表时间：
2018-08
期刊：
影响因子：
--
通讯作者：
Yan-Li Qin;Jin-Xin Zhou
中科院分区：
文献类型：
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作者：
Yan-Li Qin;Jin-Xin Zhou
如果一个图承认 $H$ 作为一组自同构群，在其具有两个轨道的顶点上半正则作用，则该图被称为群 $H$ 上的双凯莱图。对于素数 $p$，我们将元循环 $p$-群上的双凯莱图称为双-$p$-元循环。本文针对奇素数$p$刻画了连通立方边传递bi-$p$-元循环的自同构群，结果表明连通立方边传递bi-$p$-元循环仅在$p=3$时存在。使用此方法，给出了内阿贝尔元循环 $3$ 群上连通立方边传递双凯莱图的分类。结果，我们构建了第一个已知的无限族三次半对称图，其阶数为 3 美元次幂的两倍。
A graph is said to be a bi-Cayley graph over a group $H$ if it admits $H$ as a group of automorphisms acting semiregularly on its vertices with two orbits. For a prime $p$, we call a bi-Cayley graph over a metacyclic $p$-group a bi-$p$-metacirculant. In this paper, the automorphism group of a connected cubic edge-transitive bi-$p$-metacirculant is characterized for an odd prime $p$, and the result reveals that a connected cubic edge-transitive bi-$p$-metacirculant exists only when $p=3$. Using this, a classification is given of connected cubic edge-transitive bi-Cayley graphs over an inner-abelian metacyclic $3$-group. As a result, we construct the first known infinite family of cubic semisymmetric graphs of order twice a $3$-power.