Abstract
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. keywords: digraph, transitive digraph, quasi-transitive digraph, 3-transitive digraph, 3-quasi-transitive digraph, kernel. AMS Subject Classification: 05C20.
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