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.
A new 5-arc-transitive cubic graph
β Scribed by N. L. Biggs
- Book ID
- 102342841
- Publisher
- John Wiley and Sons
- Year
- 1982
- Tongue
- English
- Weight
- 188 KB
- Volume
- 6
- Category
- Article
- ISSN
- 0364-9024
No coin nor oath required. For personal study only.
β¦ Synopsis
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.
π SIMILAR VOLUMES
## Abstract A graph having 27 vertices is described, whose automorphism group is transitive on vertices and undirected edges, but not on directed edges.
Let be an X -symmetric graph admitting an X -invariant partition B on V ( ) such that B is connected and (X , 2)-arc transitive. A characterization of ( , X , B) was given in [S. Zhou Eur J Comb 23 (2002), 741-760] for the case where |B|>| (C)β©B| = 2 for an arc (B, C) of B . We consider in this arti