An infinite family of biquasiprimitive 2-arc transitive cubic graphs
Alice Devillers
, Michael Giudici
, Cai Heng Li
and Cheryl E. Praeger
DOI: 10.1007/s10801-011-0299-z
Abstract
A new infinite family of bipartite cubic 3-arc transitive graphs is constructed and studied. They provide the first known examples admitting a 2-arc transitive vertex-biquasiprimitive group of automorphisms for which the index two subgroup fixing each half of the bipartition is not quasiprimitive on either bipartite half.
Pages: 173–192
Keywords: keywords 2-arc-transitive graphs; quasiprimitive; biquasiprimitive; normal quotient; automorphism group
Full Text: PDF
References
1. Biggs, N.: Algebraic Graph Theory, 52th edn. Cambridge University Press, New York (1992)
2. Bosma, W., Cannon, J., Playoust, C.: The Magma algebra system I: the user language. J. Symb. Comput. 24(3/4), 235-265 (1997) Also see the MAGMA home page at
3. Conder, M., Nedela, R.: Symmetric cubic graphs of small girth. J. Comb. Theory, Ser. B 97(5), 757- 768 (2007)
4. Devillers, A., Giudici, M., Li, C.H., Praeger, C.E.: Locally s-distance transitive graphs. J. Graph Theory (2011).
5. Dickson, L.E.: Linear Groups: With an Exposition of the Galois Field Theory. Dover, New York (1958)
6. Dixon, J.D., Mortimer, B.: Permutation Groups. Graduate Texts in Mathematics, vol.
163. Springer, New York (1996)
7. Djoković, D.Ž., Miller, G.L.: Regular groups of automorphisms of cubic graphs. J. Comb. Theory, Ser. B 29(2), 195-230 (1980)
8. Giudici, M., Li, C.H., Praeger, C.E.: Analysing finite locally s-arc transitive graphs. Trans. Am. Math. Soc. 356, 291-317 (2004)
9. Li, C.H.: Finite s-arc transitive Cayley graphs and flag-transitive projective planes. Proc. Am. Math. Soc. 133, 31-41 (2005)
10. Lorimer, P.: Vertex-transitive graphs: symmetric graphs of prime valency. J. Graph Theory 8(1), 55-68 (1984)
11. Praeger, C.E.: Finite transitive permutation groups and bipartite vertex-transitive graphs. Ill. J. Math.
2. Bosma, W., Cannon, J., Playoust, C.: The Magma algebra system I: the user language. J. Symb. Comput. 24(3/4), 235-265 (1997) Also see the MAGMA home page at
3. Conder, M., Nedela, R.: Symmetric cubic graphs of small girth. J. Comb. Theory, Ser. B 97(5), 757- 768 (2007)
4. Devillers, A., Giudici, M., Li, C.H., Praeger, C.E.: Locally s-distance transitive graphs. J. Graph Theory (2011).
5. Dickson, L.E.: Linear Groups: With an Exposition of the Galois Field Theory. Dover, New York (1958)
6. Dixon, J.D., Mortimer, B.: Permutation Groups. Graduate Texts in Mathematics, vol.
163. Springer, New York (1996)
7. Djoković, D.Ž., Miller, G.L.: Regular groups of automorphisms of cubic graphs. J. Comb. Theory, Ser. B 29(2), 195-230 (1980)
8. Giudici, M., Li, C.H., Praeger, C.E.: Analysing finite locally s-arc transitive graphs. Trans. Am. Math. Soc. 356, 291-317 (2004)
9. Li, C.H.: Finite s-arc transitive Cayley graphs and flag-transitive projective planes. Proc. Am. Math. Soc. 133, 31-41 (2005)
10. Lorimer, P.: Vertex-transitive graphs: symmetric graphs of prime valency. J. Graph Theory 8(1), 55-68 (1984)
11. Praeger, C.E.: Finite transitive permutation groups and bipartite vertex-transitive graphs. Ill. J. Math.
© 1992–2009 Journal of Algebraic Combinatorics
©
2012 FIZ Karlsruhe /
Zentralblatt MATH for the EMIS Electronic Edition