Cubic -arc transitive Cayley graphs
β Scribed by Jing Jian Li; Zai Ping Lu
- Book ID
- 108114152
- Publisher
- Elsevier Science
- Year
- 2009
- Tongue
- English
- Weight
- 889 KB
- Volume
- 309
- Category
- Article
- ISSN
- 0012-365X
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
## Abstract In 1983, the second author [D. MaruΕ‘iΔ, Ars Combinatoria 16B (1983), 297β302] asked for which positive integers __n__ there exists a nonβCayley vertexβtransitive graph on __n__ vertices. (The term __nonβCayley numbers__ has later been given to such integers.) Motivated by this problem,
A connected cubic graph having 75,600 vertices is shown to exist, with the symmetric group S,, as a group of automorphisms acting transitively on its 5-arcs. This graph is not bipartite, nor is it a covering of any other known 4or 5-arc-transitive graph.
## Abstract A connected cubic graph with 2352 vertices is constructed and is shown to have a group of automorphisms which acts transitively on the 5βarcs. The construction requires only elementary properties of the Fano plane.