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

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

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