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A graph $G$ is said to be edge transitive provided that, for any two edges $f$ and $g$ in $G$ , there is an automorphism of $G$ sending $f$ to $g$.

Let $G$ and $H$ be two graphs on vertex sets $V(G)$ and $ V(H)$, respectively. Then their lexicographic product $ G\circ H$ is a graph denoted by $ V(G\circ H)=V(G) \times V(H) $, and there is an edge from $ (u,x) $ to $ (v,y) $ if either $ u=v $ and $ x $ be adjacent to $ y $ in $ H $, or $ u $ be adjacent to $v $ in $G $.

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