Abstract
A digraph (that is a directed graph) is said to be highly arc transitive if its automorphism group is transitive on the set ofs-arcs for eachs≥0. Several new constructions are given of infinite highly arc transitive digraphs. In particular, for Δ a connected, 1-arc transitive, bipartite digraph, a highly arc transitive digraphDL(Δ) is constructed and is shown to be a covering digraph for every digraph in a certain classD(Δ) of connected digraphs. Moreover, if Δ is locally finite, thenDL(Δ) is a universal covering digraph forD(Δ). Further constructions of infinite highly arc transitive digraphs are given.
References
G. Bergman: Private communication, 1988.
P. J. Cameron: Permutation groups with multiply transitive suborbits,Proc. London Math. Soc. (3)25 (1972), 427–440.
P. J. Cameron: Finite permutation groups and finite simple groups,Bull. London Math. Soc. 13 (1981), 1–22.
M. Hall Jr.:Combinatorial Theory, Blaisdell, Waltham, Mass., 1967.
F. Harary:Graph Theory, Addison-Wesley, New York, 1969.
W. Jackson: Private communication, 1988.
S. MacLane:Categories for the Working Mathematician, Springer-Verlag, New York, 1971.
C. E. Praeger: Highly arc transitive digraphs,Europ. J. Combinatorics 10 (1989), 281–292.
C. E. Praeger: On homomorphic images of edge transitive directed graphs,Austral. J. Combinatorics 3 (1991), 207–210.
E. H. Spanier:Algebraic Topology, McGraw Hill, New York, 1966.
Author information
Authors and Affiliations
Additional information
The second author wishes to acknowledge the hospitality of the Mathematical Institute of the University of Oxford, and the University of Auckland, during the period when the research for this paper was done
Research supported by the Australian Research Council
Rights and permissions
About this article
Cite this article
Cameron, P.J., Praeger, C.E. & Wormald, N.C. Infinite highly arc transitive digraphs and universal covering digraphs. Combinatorica 13, 377–396 (1993). https://doi.org/10.1007/BF01303511
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01303511