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A graph Γ is G-symmetric if Γ adimits G as a group of automorphisms acting transitively on the set of vertices and the set of arcs of Γ, where an arc is an ordered pair of adjacent vertices.In the case when G is imprimitive on V(Γ), namely when V(Γ) admits a nontrivial G-invariant partition β, the quotient graph Γβ of Γ with respect to tβ is always G-symmetric and sometimes even (G;2)-arc transitive.