Two-geodesic transitive graphs of order $p^n$ with $n\le 3$

Jun-Jie Huang, Yan-Quan Feng, Jin-Xin Zhou +1

A vertex triple $(u,v,w)$ of a graph is called a $2$-geodesic if $v$ is adjacent to both $u$ and $w$ and $u$ is not adjacent to $w$. A graph is said to be $2$-geodesic transitive i…