## Graph : Edge transitivity

Suppose $\Gamma (G)$ be the automorphism group of a graph $G$. Then $G$ is said to be edge transitive if for any two edges $(x,y)$ and $(u,v)$ in $G$ there exist a $f \in \Gamma (G)$ such that $f(x)=u$ and $f(y)=v$.

Let $nG$ denote the graph with $n$ components, each isomorphic to $G$.
Let $K_n(m)$ denote the complete $n$ partite graph with each partition set have $m$ points.

(1) Is $K_n(m)$ edge transitive ?
(2) Is $rK_n(m)+\ldots+rK_n(m)$ $(s times)$ edge transitive ?