Discussiones Mathematicae Graph Theory 32(2) (2012) 205-219
doi: 10.7151/dmgt.1613

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3-transitive Digraphs

César Hernández-Cruz

Instituto de Matemáticas
Universidad Nacional Autónoma de México
Ciudad Universitaria, México, D.F., C.P. 04510, México

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, kernel, transitive digraph, quasi-transitive digraph, 3-transitive digraph, 3-quasi-transitive digraph

2010 Mathematics Subject Classification: 05C20.

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Received 16 February 2011
Revised 02 April 2011
Accepted 04 April 2011