Elsevier

Discrete Mathematics

Volume 309, Issue 17, 6 September 2009, Pages 5404-5410
Discrete Mathematics

Classification of a family of symmetric graphs with complete 2-arc-transitive quotients

https://doi.org/10.1016/j.disc.2008.12.001Get rights and content
Under an Elsevier user license
open archive

Abstract

In this paper we give a classification of a family of symmetric graphs with complete 2-arc-transitive quotients. Of particular interest are two subfamilies of graphs which admit an arc-transitive action of a projective linear group. The graphs in these subfamilies can be defined in terms of the cross ratio of certain 4-tuples of elements of a finite projective line, and thus may be called the second type ‘cross ratio graphs’, which are different from the ‘cross ratio graphs’ studied in [A. Gardiner, C. E. Praeger, S. Zhou, Cross-ratio graphs, J. London Math. Soc. (2) 64 (2001), 257–272]. We also give a combinatorial characterisation of such second type cross ratio graphs.

Keywords

Symmetric graph
Arc-transitive graph
2-arc-transitive graph
Quotient graph
3-arc graph
Cross ratio graph

Cited by (0)