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When are symmetric graphs characterised by their local properties?

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References

  1. C. Armanios, Symmetric graphs and their automorphism groups, thesis, Univ. of Western Australia, Perth, 1981.

    Google Scholar 

  2. F. Buekenhout and X. Hubaut, Locally polar spaces and related rank 3 groups, J. Algebra 45 (1977) 391–434.

    Article  MathSciNet  MATH  Google Scholar 

  3. M. Bürker and W. Knapp, Zur Vermutung von Sims über primitive Permutationsgruppen II, Arch. Math. 27 (1976) 352–359.

    Article  MATH  Google Scholar 

  4. W. Burnside, Theory of groups of finite order, (Cambridge University Press, Cambridge, 1911).

    MATH  Google Scholar 

  5. P.J. Cameron, Permutation groups with multiply transitive suborbits, Proc. London Math. Soc. (3) 25 (1972) 427–440.

    Article  MathSciNet  MATH  Google Scholar 

  6. P.J. Cameron, Suborbits in transitive permutation groups, in Combinatorial Group Theory, ed. M. Hall Jr. and J.H. Van Lint, Math. Centre Tracts No. 57, (Math. Centrum, Amsterdam, 1974), 98–129.

    Google Scholar 

  7. P.J. Cameron, Finite permutation groups and finite simple groups, Bull. London Math. Soc. 13 (1981) 1–22.

    Article  MathSciNet  MATH  Google Scholar 

  8. P.J. Cameron and C.E. Praeger, Graphs and permutation groups with projective subconstituents, J. London Math. Soc. (to appear).

    Google Scholar 

  9. P.J. Cameron and C.E. Praeger, On 2-arc transitive graphs of girth 4, (submitted).

    Google Scholar 

  10. J.I. Hall, Locally Petersen graphs, J. Graph Theory (to appear).

    Google Scholar 

  11. M. Hall Jr. and E. Shult, Locally cotriangular graphs, in Finite Geometries and Designs, ed. P.J. Cameron, J. Hirshfeld, and D. Hughes, LMS Lecture Notes, London, 1981, (to appear).

    Google Scholar 

  12. R.W. Hartley, Determination of the ternary collineation groups whose coefficients lie in GF(2n), Ann. Math. 27 (1925) 140–158.

    Article  MathSciNet  MATH  Google Scholar 

  13. W. Kantor, Symplectic groups, symmetric designs, and line ovals, J. Algebra 33 (1975) 43–58.

    Article  MathSciNet  MATH  Google Scholar 

  14. W. Knapp, On the point stabilizer in a primitive permutation group, Math. Z. 133 (1973) 137–168.

    Article  MathSciNet  MATH  Google Scholar 

  15. H. Lüneberg, Die Suzukigruppen und ihre Geometrien, Lecture Notes In Math. 10 (Springer-Verlag, Berlin-Heidelberg-New York, 1965).

    Google Scholar 

  16. H.H. Mitchell, Determination of the ordinary and modular ternary linear groups, Trans. Amer. Math. Soc. 12 (1911) 207–242.

    Article  MathSciNet  MATH  Google Scholar 

  17. I. Miyamoto, On primitive permutation groups with a rank 3 suborbit, in International Symposium on Theory of Finite Groups, Japan, 79–82.

    Google Scholar 

  18. M. O'Nan, Normal structure of the one-point stabilizer of a doubly-transitive permutation group II, Trans. Amer. Math. Soc. 214 (1975) 43–74.

    Article  MathSciNet  MATH  Google Scholar 

  19. C.E. Praeger, Primitive permutation groups and a characterization of the odd graphs, J. Combin. Theory, Series B, 31 (1981) 117–142.

    Article  MathSciNet  MATH  Google Scholar 

  20. C.E. Praeger, Symmetric graphs and a characterization of the odd graphs, in Combinatorial Mathematics VII, ed. by R.W. Robinson, G.W. Southern, and W.D. Wallis, Lecture Notes in Math. 829 (Springer-Verlag, Berlin, Heidelberg, New York, 1980), 211–219.

    Chapter  Google Scholar 

  21. E. Shult, Groups, polar spaces and related structures, Math. Centre Tracts 57 (1974) 130–161.

    MathSciNet  MATH  Google Scholar 

  22. H. Wielandt, Finite Permutation Groups,(Academic Press, New York, 1964).

    MATH  Google Scholar 

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Elizabeth J. Billington Sheila Oates-Williams Anne Penfold Street

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© 1982 Springer-Verlag

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Praeger, C.E. (1982). When are symmetric graphs characterised by their local properties?. In: Billington, E.J., Oates-Williams, S., Street, A.P. (eds) Combinatorial Mathematics IX. Lecture Notes in Mathematics, vol 952. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0061976

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  • DOI: https://doi.org/10.1007/BFb0061976

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-11601-1

  • Online ISBN: 978-3-540-39375-7

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