Direct product of automorphism groups of digraphs
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Authors
Organisational units
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 language | English |
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Pages (from-to) | 89-101 |
Number of pages | 13 |
Journal | Ars mathematica contemporanea |
Volume | 17.2019 |
Issue number | 1 |
DOIs | |
Publication status | Published - 1 Jan 2019 |