论文标题
两极传递双回路
Two-arc-transitive bicirculants
论文作者
论文摘要
在本文中，我们确定有限的2 Arc传播双相的类别。我们表明，连接的$ 2 $ -ARC传播双环是以下图表之一：$ c_ {2n} $其中$ n \ geqslant 2 $，$ \ k_ {2n} $其中$ n \ geqslant 2 $，$ \ k_ {n，n} $ \ 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 $是主要功率， $ x_1（4，q）$其中$ q \ equiv 3 \ pmod {4} $是主要功率 $ \ k_ {q+1}^{2d} $其中$ q $是一种奇怪的质量功率，$ d \ geq 2 $ dividing $ q-1 $，$ at_q（1+q，2d）$其中$ d \ d \ d \ d \ d \ d \ d \ d \ d \ d \ nmid \ nmid \ frac \ frac {1}}（Q-1} {2}（Q-1）$，$，$，$，$，$，$，1+at d \ at d d \ at d+ \ frac {1} {2}（q-1）$和$ 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）$和$ at_d（5,6）$。
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)$.
