On a class of finite symmetric graphs

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 2 {dot operator} K2 or K2, 2. The results answer two questions about the relationship between Γ and ΓB for this class of graphs. © 2007 Elsevier Ltd. All rights reserved.