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2012•Discussiones Mathematicae Graph TheoryOpen access

3-transitive digraphs

César Hernández‐Cruz

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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.

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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.

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Available 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.

Key concepts: Digraph, Transitive relation, Combinatorics, Mathematics, Kernel (algebra), Transitive reduction, Discrete mathematics, Transitive closure

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