Direct product of automorphism groups of digraphs

Research output: Contribution to journalArticleResearchpeer-review

Authors

External Organisational units

  • 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

Original languageEnglish
Pages (from-to)89-101
Number of pages13
JournalArs mathematica contemporanea
Volume17.2019
Issue number1
DOIs
Publication statusPublished - 1 Jan 2019