Name
Abstract | ||
|---|---|---|
Given a colouring Δ of a d -regular digraph G and a colouring Π of the symmetric complete digraph on d vertices with loops, the uniformly induced colouring L Π Δ of the line digraph LG is defined. It is shown that the group of colour-preserving automorphisms of ( LG , L Π Δ ) is a subgroup of the group of colour-permuting automorphisms of ( G , Δ ). This result is then applied to prove that if ( G , Δ ) is a d -regular coloured digraph and ( LG , L Π Δ ) is a Cayley digraph, then ( G , Δ ) is itself a Cayley digraph Cay (Ω, Δ) and Π is a group of automorphisms of Ω. In particular, a characterization of those Kautz digraphs which are Cayley digraphs is given. If d =2, for every arc-transitive digraph G , LG is a Cayley digraph when the number k of orbits by the action of the so-called Rankin group is at most 5. If k ⩾ 3 the arc-transitive k -generalized cycles for which LG is a Cayley digraph are characterized. |
Year | DOI | Venue |
|---|---|---|
1995 | 10.1016/0012-365X(94)00196-P | Discrete Mathematics |
Keywords | Field | DocType |
cayley line digraph | Discrete mathematics,Combinatorics,Vertex (geometry),Automorphism,Cayley's theorem,Cayley digraphs,Mathematics,Digraph | Journal |
Volume | Issue | ISSN |
138 | 1 | Discrete Mathematics |
Citations | PageRank | References |
2 | 0.51 | 2 |
Authors | ||
4 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| J. M. Brunat | 1 | 15 | 3.08 |
| M. Espona | 2 | 13 | 1.69 |
| M. A. Fiol | 3 | 816 | 87.28 |
| O. Serra | 4 | 89 | 13.05 |