Direct product of automorphism groups of digraphs

Publikationen: Beitrag in FachzeitschriftArtikelForschung(peer-reviewed)

Autoren

Externe Organisationseinheiten

  • University of Wrocław
  • Wrocław University of Science and Technology
  • Nokia Networks

Abstract

We study the direct product of automorphism groups of digraphs, where automorphism groups are considered as permutation groups acting on the sets of vertices. By a direct product of permutation groups (A, V ) × (B, W) we mean the group (A × B, V × W) acting on the Cartesian product of the respective sets of vertices. We show that, except for the infinite family of permutation groups Sn × Sn, n ≥ 2, and four other permutation groups, namely D4 × S2, D4 × D4, S4 × S2 × S2, and C3 × C3, the direct product of automorphism groups of two digraphs is itself the automorphism group of a digraph. In the course of the proof, for each set of conditions on the groups A and B that we consider, we indicate or build a specific digraph product that, when applied to the digraphs representing A and B, yields a digraph whose automorphism group is the direct product of A and B.

Details

OriginalspracheEnglisch
Seiten (von - bis)89-101
Seitenumfang13
FachzeitschriftArs mathematica contemporanea
Jahrgang17.2019
Ausgabenummer1
DOIs
StatusVeröffentlicht - 1 Jan. 2019