5-arc transitive cubic Cayley graphs on finite simple groups. (English) Zbl 1113.05049
Summary: We determine all connected 5-arc transitive cubic Cayley graphs on the alternating group A\(_{47}\); there are only two such graphs (up to isomorphism). By earlier work of the authors, these are the only two non-normal connected cubic arc-transitive Cayley graphs for finite nonabelian simple groups, and so this paper completes the classification of such non-normal Cayley graphs.
MSC:
| 05C25 | Graphs and abstract algebra (groups, rings, fields, etc.) |
References:
| [1] | Xu, S. J.; Fang, X. G.; Wang, J.; Xu, M. Y., On cubic s-arc-transitive Cayley graphs of finite simple groups, European J. Combin., 26, 133-143 (2005) · Zbl 1060.05043 |
| [2] | Xu, M.-Y., Automorphism groups and isomorphisms of Cayley digraphs, Discrete Math., 182, 309-319 (1998) · Zbl 0887.05025 |
| [3] | Biggs, N., Algebraic Graph Theory (1974), Cambridge University Press, Second edition 1993 · Zbl 0284.05101 |
| [4] | C.H. Li, Isomorphisms of finite Cayley graphs, Ph.D. Thesis, The University of Western Australia, 1996; C.H. Li, Isomorphisms of finite Cayley graphs, Ph.D. Thesis, The University of Western Australia, 1996 |
| [5] | Babai, L., Isomorphism problem for a class of point-symmetric structures, Acta Math. Acad. Sci. Hungar, 29, 329-336 (1977) · Zbl 0378.05035 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
