Discussiones Mathematicae Graph Theory 33(2) (2013)
247-260

doi: 10.7151/dmgt.1645

César Hernández-Cruz
Instituto de Matemáticas |

In this work, some general structural results are proved for k-transitive digraphs with arbitrary k ≥ 2. Some of this results are used to characterize the family of 4-transitive digraphs. Also some of the general results remain valid for k-quasi-transitive digraphs considering an additional hypothesis. A conjecture on a structural property of k-transitive digraphs is proposed.

**Keywords:** digraph, transitive digraph, quasi-transitive digraph, *4*-transitive digraph, *k*-transitive digraph, *k*-quasi-transitive digraph

**2010 Mathematics Subject Classification:** 05C20, 05C75.

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Received 25 May 2011

Revised 22 February 2012

Accepted 23 February 2012