Infinite highly arc transitive digraphs and universal covering digraphs
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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.
- 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.
- Infinite highly arc transitive digraphs and universal covering digraphs
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- Author Affiliations
- 1. School of Mathematical Sciences, Queen Mary and Westfield College, Mile End Road, E1 4NS, London, UK
- 2. Department of Mathematics, University of Western Australia, 6009, Nedlands, W.A., Australia
- 3. Department of Mathematics, University of Melbourne, 3052, Parkville, VIC, Australia