arXiv 2211.145202022-11-26math.COmath.GR

双弧传递双循环

Two-arc-transitive bicirculants

Wei Jin

备注：: arXiv admin note: text overlap with arXiv:1904.06467

摘要：

本文确定了有限2-弧传递双循环的类。我们证明了一个连通的$2$ -弧传递双循环图是下列图之一：$C_{2n}$其中$n\geqslant 2$，$\K_{2n}$其中$n\geqslant 2$，$\K_{n,n}$其中$n\geqslant 3$，$ \K_{n,n}-n\K_2$其中$n\geqslant 4$，$B(\PG(d-1,q))$和$B'(\PG(d-1,q))$其中$d\geq 3$和$q$是素数幂，$ X_1(4,q)$其中$q\equiv 3\pmod{4}$是素数幂，$\K_{q+1}^{2d}$其中$q$是奇数素数幂，$d\geq 2$划分$q-1$，$ AT_Q(1+q,2d)$其中$d\mid q-1$和$d\nmid \frac{1}{2}(q-1)$，$ AT_D(1+q,2d)$其中$d\mid \frac{1}{2}(q-1)$和$d\geq 2$，$Γ(d, q, r)$，其中$d\geq 2$，$q$是素数幂和$r|q-1$，Petersen图，Desargues图，十二面体图，折叠$5$ -立方体，$X(3,2)$，$ X_2(3)$，$ AT_Q(4,12)$，$GP(12,5)$，$GP(24,5)$，$B(H(11))$，$B'(H(11))$，$ AT_D(4,6)$和$ AT_D(5,6)$。

英文摘要：

In this paper, we determine the class of finite 2-arc-transitive bicirculants. We show that a connected $2$-arc-transitive bicirculant is one of the following graphs: $C_{2n}$ where $n\geqslant 2$, $\K_{2n}$ where $n\geqslant 2$, $\K_{n,n}$ where $n\geqslant 3$, $ \K_{n,n}-n\K_2$ where $n\geqslant 4$, $B(\PG(d-1,q))$ and $B'(\PG(d-1,q))$ where $d\geq 3$ and $q$ is a prime power, $ X_1(4,q)$ where $q\equiv 3\pmod{4}$ is a prime power, $\K_{q+1}^{2d}$ where $q$ is an odd prime power and $d\geq 2$ dividing $q-1$, $ AT_Q(1+q,2d)$ where $d\mid q-1$ and $d\nmid \frac{1}{2}(q-1)$, $ AT_D(1+q,2d)$ where $d\mid \frac{1}{2}(q-1)$ and $d\geq 2$, $Γ(d, q, r)$, where $d\geq 2$, $q$ is a prime power and $r|q-1$, Petersen graph, Desargues graph, dodecahedron graph, folded $5$-cube, $X(3,2)$, $ X_2(3)$, $ AT_Q(4,12)$, $GP(12,5)$, $GP(24,5)$, $B(H(11))$, $B'(H(11))$, $ AT_D(4,6)$ and $ AT_D(5,6)$.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

摘要：

英文摘要：

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