Let $x=\{1,2,3,4,5\}, V_{1}=X \times\{0,1\}$ and $V_{2}$ be the set of 2-subsets of $X$. Let $G$ be the bipartite graph with vertex-set $V_{1} \cup V_{2}$, with $(x, i) \in V_{1}$ adjacent to $\{y, zl} \in V_{2}$ if and only if $x \in\{y, z\}$. Show that $G$ is a 4-regular graph of order 20 that is edge-transitive but not vertex-transitive. CS.VS. 1409|