paper

Two-arc-transitive bicirculants

arXiv:2211.14520

Abstract

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: $C_{2 n}$ where $n ⩾ 2$ , $\K_{2n}$ where $n ⩾ 2$ , $\K_{n,n}$ where $n ⩾ 3$ , $ \K_{n,n}-n\K_2$ where $n ⩾ 4$ , $B(\PG(d-1,q))$ and $B'(\PG(d-1,q))$ where $d \geq 3$ and $q$ is a prime power, $X_{1} (4, q)$ where $q \equiv 3 (mod 4)$ is a prime power, $\K_{q+1}^{2d}$ where $q$ is an odd prime power and $d \geq 2$ dividing $q - 1$ , $A T_{Q} (1 + q, 2 d)$ where $d ∣ q - 1$ and $d ∤ \frac{1}{2} (q - 1)$ , $A T_{D} (1 + q, 2 d)$ where $d ∣ \frac{1}{2} (q - 1)$ and $d \geq 2$ , $I^ (d, q, r)$ , where $d \geq 2$ , $q$ is a prime power and $r ∣ q - 1$ , Petersen graph, Desargues graph, dodecahedron graph, folded $5$ -cube, $X (3, 2)$ , $X_{2} (3)$ , $A T_{Q} (4, 12)$ , $GP (12, 5)$ , $GP (24, 5)$ , $B (H (11))$ , $B^{'} (H (11))$ , $A T_{D} (4, 6)$ and $A T_{D} (5, 6)$ .

arXiv admin note: text overlap with arXiv:1904.06467