A class of symmetric graphs with 2-ARC transitive quotients

Abstract

Let Γ be an X-symmetric graph admitting an X-invariant partition ß on V(T) such that Γß is connected and (X, 2)-arc transitive. A characterization of (T,X,ß) was given in [S. Zhou Eur J Comb 23(2002), 741-760] for the case where |B|>|Γ(C)∪B|=2 for an arc (B, C) of ΓB. We consider in this article the case where |B|>|Γ(C)∪B|=3, and prove that Γ can be constructed from a 2-arc transitive graph of valency 4 or 7 unless its connected components are isomorphic to 3K2, C6 or K3,3. As a byproduct, we prove that each connected tetravalent (X, 2)-transitive graph is either the complete graph K5 or a near n-gonal graph for some n≥4. © 2010 Wiley Periodicals, Inc.