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 3-transitive if the existence of the directed path (u,v,w,x) of length 3 in D implies the existence of the arc (u,x) ∈ A(D). In this article strong 3-transitive digraphs are characterized and the structure of non-strong 3-transitive digraphs is described. The results are used, e.g., to characterize 3-transitive digraphs that are transitive and to characterize 3-transitive digraphs with a kernel.
@article{bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1613,
author = {C\'esar Hern\'andez-Cruz},
title = {3-transitive digraphs},
journal = {Discussiones Mathematicae Graph Theory},
volume = {32},
year = {2012},
pages = {205-219},
zbl = {1255.05087},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1613}
}
César Hernández-Cruz. 3-transitive digraphs. Discussiones Mathematicae Graph Theory, Tome 32 (2012) pp. 205-219. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1613/
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