This paper classifies all finite edge colored graphs with doubly transitive automorphism groups. This result generalizes the classification of doubly transitive balanced incomplete block designs with λ=1 and doubly transitive one-factorizations of complete graphs. It also provides a classification of all doubly transitive symmetric association schemes.
Copyright © 2003 Elsevier Inc. All rights reserved. NOTICE: this is the author’s version of a work that was accepted for publication in Journal of Combinatorial Theory, Series B. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Journal of Combinatorial Theory, Series B 90(1): 121-138, January 2004. DOI: 10.1016/S0095-8956(03)00079-0
Sibley TQ. 2004. On classifying finite edge colored graphs with two transitive automorphism groups. Journal of Combinatorial Theory, Series B 90(1): 121-138.