On automorphism groups of quasiprimitive 2-arc transitive graphs
Cai Heng Li
The University of Western Australia School of Mathematics and Statistics Crawley WA 6009 Australia
DOI: 10.1007/s10801-007-0101-4
Abstract
We characterize the automorphism groups of quasiprimitive 2-arc-transitive graphs of twisted wreath product type. This is a partial solution for a problem of Praeger regarding quasiprimitive 2-arc transitive graphs. The solution stimulates several further research problems regarding automorphism groups of edge-transitive Cayley graphs and digraphs.
Pages: 261–270
Keywords: keywords quasiprimitive; 2-arc transitive; automorphisms; Cayley graphs
Full Text: PDF
References
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9. Li, C.H.: Finite s-arc transitive graphs of prime-power order. Bull. Lond. Math. Soc. 33, 129-137 (2001)
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2. Baddeley, R.W., Praeger, C.E.: On primitive overgroups of quasiprimitive permutation groups. J. Al- gebra 263, 291-361 (2003)
3. Cameron, P.: Permutation Groups. London Mathematical Society Student Texts, vol. 45, Cambridge University Press, Cambridge (1999)
4. Fang, X.G., Li, C.H., Wang, J., Xu, M.Y.: On cubic Cayley graphs of finite simple groups. Discrete Math. 244, 67-75 (2002)
5. Fang, X.G., Havas, G., Wang, J.: A family of non-quasiprimitive graphs admitting a quasiprimitive 2-arc transitive group action. Eur. J. Comb. 20, 551-557 (1999)
6. Godsil, C.D.: On the full automorphism group of a graph. Combinatorica 1, 243-256 (1981)
7. Ivanov, A.A., Praeger, C.E.: On finite affine 2-arc transitive graphs. Eur. J. Comb. 14, 421-444 (1993)
8. Li, C.H.: A family quasiprimitive 2-arc-transitive graphs which have non-quasiprimitive full automorphism groups. Eur. J. Comb. 19, 499-502 (1998)
9. Li, C.H.: Finite s-arc transitive graphs of prime-power order. Bull. Lond. Math. Soc. 33, 129-137 (2001)
10. Li, C.H.: On isomorphisms of finite Cayley graphs-a survey. Discrete Math. 256, 301-334 (2002)
11. Li, C.H.: On finite edge-transitive Cayley graphs and rotary Cayley maps. Trans. Am. Math. Soc. 358, 4605-4635 (2006)
12. Li, C.H., Seress, A.: Constructions of quasiprimitive two-arc transitive graphs of product action type. In: Finite Geometries, Groups and Computation, pp. 115-124 (2006)
13. Praeger, C.E.: An O'Nan-Scott theorem for finite quasiprimitive permutation groups and an application to 2-arc transitive graphs. J. Lond. Math. Soc. 47, 227-239 (1992)
14. Praeger, C.E.: On a reduction theorem for finite, bipartite 2-arc-transitive graphs. Australas. J. Comb. 7, 21-36 (1993)
15. Praeger, C.E.: Finite quasiprimitive graphs. In: Surveys in Combinatorics 1997, London. London Mathematical Society Lecture Notes series, vol. 241, pp. 65-85. Cambridge University Press, Cambridge (1997) J Algebr Comb (2008) 28: 261-270