A group G admits an n-partite digraphical representation if there exists a regular n-partite digraph Γ such that the automorphism group Aut(Γ) of Γ satisfies the following properties: (1) Aut(Γ) is isomorphic to G, (2) Aut(Γ) acts semiregularly on the vertices of Γ and (3) the orbits of Aut(Γ) on the vertex set of Γ form a partition into n parts giving a structure of n-partite digraph to Γ. In this paper, for every positive integer n, we classify the finite groups admitting an n-partite digraphical representation.
Du, J., Feng, Y., Spiga, P. (2022). On n-partite digraphical representations of finite groups. JOURNAL OF COMBINATORIAL THEORY. SERIES A, 189(July 2022) [10.1016/j.jcta.2022.105606].
On n-partite digraphical representations of finite groups
Spiga P.
2022
Abstract
A group G admits an n-partite digraphical representation if there exists a regular n-partite digraph Γ such that the automorphism group Aut(Γ) of Γ satisfies the following properties: (1) Aut(Γ) is isomorphic to G, (2) Aut(Γ) acts semiregularly on the vertices of Γ and (3) the orbits of Aut(Γ) on the vertex set of Γ form a partition into n parts giving a structure of n-partite digraph to Γ. In this paper, for every positive integer n, we classify the finite groups admitting an n-partite digraphical representation.
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