On Cayley line digraphs

✍ Scribed by J.M. Brunat; M. Espona; M.A. Fiol; O. Serra

• Publisher: Elsevier Science
• Year: 1995
• Tongue: English
• Weight: 657 KB
• Volume: 138
• Category: Article
• ISSN: 0012-365X
• DOI: 10.1016/0012-365x(94)00196-p

✦ Synopsis

Given a colouring A of a d-regular digraph G and a colouring H of the symmetric complete digraph on d vertices with loops, the uniformly induced colouring LnA of the line digraph LG is defined. It is shown that the group of colour-preserving automorphisms of (LG, L,A) is a subgroup of the group of colour-permuting automorphisms of (G,A). This result is then applied to prove that if (G,A) is a d-regular coloured digraph and (LG, LIIA) is a Cayley digraph, then (G, A ) is itself a Cayley digraph Cay (Q, A ) and H is a group of automorphisms of f2. 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.