On a class of finite symmetric graphs

Let Γ be a G -symmetric graph, and let B be a nontrivial G -invariant partition of the vertex set of Γ . This paper aims to characterize ( Γ , G ) under the conditions that the quotient graph Γ B is ( G , 2 ) -arc transitive and the induced subgraph between two adjacent blocks is 2 ⋅ K 2 or K 2 , 2 . The results answer two questions about the relationship between Γ and Γ B for this class of graphs.