Two-arc-transitive bicirculants

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 $n⩾2$, ${\text{K}}_{2n}$ where $n⩾2$, ${\text{K}}_{n,n}$ where $n⩾3$, ${\text{K}}_{n,n}-n{\text{K}}_2$ where $n⩾4$, $B(\text{PG}(d-1,q))$ and $B^{\mathrm{\prime }}(\text{PG}(d-1,q))$ where $d\ge 3$ and $q$ is a prime power, $X_1(4,q)$ where $q\equiv 3(\mathrm{m}\mathrm{o}\mathrm{d}4)$ is a prime power, ${\text{K}}_{q+1}^{2d}$ where $q$ is an odd prime power and $d\ge 2$ dividing $q-1$, $A{T}_Q(1+q,2d)$ where $d\mid q-1$ and $d\nmid \frac{1}{2}(q-1)$, $A{T}_D(1+q,2d)$ where $d\mid \frac{1}{2}(q-1)$ and $d\ge 2$, $\mathrm{\Gamma }(d,q,r)$, where $d\ge 2$, $q$ is a prime power and $r\mathrm{\mid }q-1$, Petersen graph, Desargues graph, dodecahedron graph, folded $5$-cube, $X(3,2)$, $X_2(3)$, $A{T}_Q(4,12)$, $GP(12,5)$, $GP(24,5)$, $B(H(11))$, $B^{\mathrm{\prime }}(H(11))$, $A{T}_D(4,6)$ and $A{T}_D(5,6)$.