On a class of finite symmetric graphs

Dedicated to Professor Yixun Lin with best wishes on the occasion of his 70th birthday
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Abstract

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 ΓB is (G,2)-arc transitive and the induced subgraph between two adjacent blocks is 2K2 or K2,2. The results answer two questions about the relationship between Γ and ΓB for this class of graphs.

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