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Constructing continuum many countable, primitive, unbalanced digraphs. (English) Zbl 1213.05110

Summary: We construct continuum many non-isomorphic countable digraphs which are highly arc transitive, have finite out-valency and infinite in-valency, and whose automorphism groups are primitive.

MSC:

05C20 Directed graphs (digraphs), tournaments
05C63 Infinite graphs
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References:

[1] Daniela Amato, D. Phil. Thesis, University of Oxford, 2006; Daniela Amato, D. Phil. Thesis, University of Oxford, 2006
[2] Daniela Amato, Descendants in primitive and highly arc-transitive digraphs, Preprint, University of Leeds, February 2008; Daniela Amato, Descendants in primitive and highly arc-transitive digraphs, Preprint, University of Leeds, February 2008 · Zbl 1222.05079
[3] Daniela Amato, John Truss, Some constructions of highly arc-transitive digraphs, Preprint, University of Leeds, June 2008; Daniela Amato, John Truss, Some constructions of highly arc-transitive digraphs, Preprint, University of Leeds, June 2008 · Zbl 1249.05160
[4] Cameron, Peter J.; Praeger, Cheryl E.; Wormald, Nicholas C., Infinite highly arc transitive digraphs and universal covering digraphs, Combinatorica, 13, 4, 377-396 (1993) · Zbl 0793.05065
[5] Evans, David M., Suborbits in infinite primitive permutation groups, Bull. London Math. Soc., 33, 583-590 (2001) · Zbl 1029.20002
[6] Evans, David M., An infinite highly arc-transitive digraph, European J. Combin., 18, 281-286 (1997) · Zbl 0873.05050
[7] Higman, D. G., Intersection matrices for finite permutation groups, J. Algebra, 6, 22-42 (1967) · Zbl 0183.02704
[8] Neumann, Peter M., Postscript to review of oligomorphic permutation groups by Peter J. Cameron, Bull. London Math. Soc., 24, 404-407 (1992)
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