Let D be a digraph, V (D) and A(D) will denote the sets of vertices and arcs of D, respectively. A digraph D is transitive if for every three distinct vertices u, v,w ∈ V (D), (u, v), (v,w) ∈ A(D) implies that (u,w) ∈ A(D). This concept can be generalized as follows: A digraph is k-transitive if for every u, v ∈ V (D), the existence of a uv-directed path of length k in D implies that (u, v) ∈ A(D). A very useful structural characterization of transitive digraphs has been known for a long time, and recently, 3-transitive digraphs have been characterized. 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.
@article{bwmeta1.element.doi-10_7151_dmgt_1645,
author = {C\'esar Hern\'andez-Cruz},
title = {4-Transitive Digraphs I: The Structure of Strong 4-Transitive Digraphs},
journal = {Discussiones Mathematicae Graph Theory},
volume = {33},
year = {2013},
pages = {247-260},
zbl = {1293.05136},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_7151_dmgt_1645}
}
César Hernández-Cruz. 4-Transitive Digraphs I: The Structure of Strong 4-Transitive Digraphs. Discussiones Mathematicae Graph Theory, Tome 33 (2013) pp. 247-260. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_7151_dmgt_1645/
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