A classification of two-distance-transitive Cayley graphs over the generalized quaternion groups

Wei Jin, Pingshan Li, Li Tan

A non-complete graph is \emph{$2$-distance-transitive} if, for $i=1,2$ and for any two vertex pairs $(u_1,v_1)$ and $(u_2,v_2)$ with the same distance $i$ in the graph, there exist…