Abstract
For a prime p at least 5, let T = PSL(2, p). This paper gives a classification of the connected arc-transitive cubic Cayley graphs on T and a determination of the generated pairs (ā,−) of T such that o(ā) = 2 and o(−)= 3.
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References
Biggs, N. L., Algebraic Graph Theory, Cambridge: Cambridge University Press, 1974.
Huppert, B., Endliche Gruppen I, Berlin: Springer-Verlag, 1967.
Tutte, W. T., A family of cubic graphs, Proc. Cambr. Philosoph. Soc., 1947, 43: 459–474.
Tutte, W. T., On the symmetry of cubic graphs, Can. J. Math. 1959, 11: 621–624.
Conder, M. D. E., Lorimer, P., Automorphism groups of symmetric graphs of valency 3, J. Combin. Theory (B), 1989, 47: 60–72.
Conder, M. D. E., Praeger, C. E., Remarks on path-transitivity on finite graphs, Europ. J. Combin., 1996, 17: 371–378.
Djoković, D. Ž., Miller, G. L., Regular groups of automorphisms of cubic graphs, J. Combin. Theory (B), 1980, 29: 195–230.
Frucht, R., A one-regular graph of degree three, Canad. J. Math., 1952, 4: 240–247.
Gosil, C. D., The automorphism groups of some cubic Cayley graphs, Europ. J. Combin., 1983, 4: 25–32.
Miller, R. C., The trivalent symmetric graphs of girth at most six, J. Combin. Theory (B), 1971, 10: 163–182.
Marušič, D., Pisanski, P., Symmetries of hexagonal molecular graphs on the torus, Croat. Chemica Acta., 2000, 72: 69–82.
Fang, X. G., Li, C. H., Wang, J. et al., On cubic normal Cayley graphs of finite simple groups, Discrete Math., 2002, 244: 67–75.
Xu, S. J., Fang, X. G., Wang, J. et al., On cubic s-arc-transtive Cayley graphs of finite simple groups, Euro J. of Combin., 2005, 26: 133–143.
Xu, M. Y., Xu, S. J., The symmetry properties of Cayley graphs of small valencies on the alternating group A 5, Sci. China, Ser. A, 2004, 47: 593–604.
Xu, M. Y., Automorphism groups and isomorphisms of Cayley digraphs, Discrete Math., 1998, 182: 309–319.
Dickson, L. E., Linear Groups with an exposition of the Galois field theory, Leipzig, 1901; Dover Publ. 1958.
Pan, C. D., Pan, C. B., Elementary Number Theory (in Chinese), Beijing: Beijing University Press, 1992.
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Du, S., Wang, F. Arc-transitive cubic cayley graphs on PSL(2, p). Sci. China Ser. A-Math. 48, 1297–1308 (2005). https://doi.org/10.1360/03ys0374
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DOI: https://doi.org/10.1360/03ys0374