Name
Title | ||
|---|---|---|
Vertex-transitive digraphs with extra automorphisms that preserve the natural arc-colouring. |
Abstract | ||
|---|---|---|
In a Cayley digraph on a group G, if a distinct colour is assigned to each arc-orbit under the left-regular action of G, it is not hard to show that the elements of the left-regular action of G are the only digraph auto-morphisms that preserve this colouring. In this paper, we show that the equivalent statement is not true in the most straightforward generalisation to G-vertex-transitive digraphs, even if we restrict the situation to avoid some obvious potential problems. Specifically, we display an infinite family of 2-closed groups G, and a G-arc-transitive digraph on each (without any digons) for which there exists an automorphism of the digraph that is not an element of G (it is an automorphism of G). Since the digraph is G-arc-transitive, the arcs would all be assigned the same colour under the colouring by arc-orbits, so this digraph automorphism is colour-preserving. |
Year | Venue | DocType |
|---|---|---|
2017 | AUSTRALASIAN JOURNAL OF COMBINATORICS | Journal |
Volume | ISSN | Citations |
67 | 2202-3518 | 0 |
PageRank | References | Authors |
0.34 | 0 | 4 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Ted Dobson | 1 | 1 | 1.38 |
| Ademir Hujdurović | 2 | 18 | 10.06 |
| Klavdija Kutnar | 3 | 138 | 24.35 |
| Joy Morris | 4 | 78 | 16.06 |