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Classifying distance-transitive graphs

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References

  1. L.W. Beineke and R.J. Wilson (eds.), Selected topics in graph theory, Academic Press, 1978.

    Google Scholar 

  2. N.L. Biggs, Finite groups of automorphisms, London Math. Soc. Lecture Notes 6, Cambridge University Press, 1971.

    Google Scholar 

  3. N.L. Biggs, Algebraic graph theory, Cambridge University Press, 1974.

    Google Scholar 

  4. N.L. Biggs, Automorphic graphs and the Krein condition, Geometriae Dedicata 5 (1976), 117–127.

    CrossRef  MathSciNet  MATH  Google Scholar 

  5. N.L. Biggs, The symmetry of line graphs, Utilitas Mathematica 5 (1974), 113–121.

    MathSciNet  MATH  Google Scholar 

  6. N.L. Biggs and D.H. Smith, On trivalent graphs, Bull. London Math. Soc. 3 (1971), 155–158.

    CrossRef  MathSciNet  MATH  Google Scholar 

  7. P.J. Cameron, A note on distance-transitive graphs, (to appear).

    Google Scholar 

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

    CrossRef  MathSciNet  MATH  Google Scholar 

  9. P.J. Cameron, C.E. Praeger, J. Saxl, G. Seitz, (in preparation).

    Google Scholar 

  10. A. Gardiner, On trivalent graphs, J. London Math. Soc. (2) 10 (1975) 507–512.

    CrossRef  MathSciNet  MATH  Google Scholar 

  11. A. Gardiner, When is an array realised by a distance-regular graph, Colloquia Mathematica Societatis János Bolyai 25, Szeged, 1978.

    Google Scholar 

  12. A. Gardiner, Arc transitivity in graphs, Quart. J. Math. (Oxford) (2) 24 (1973), 399–407.

    CrossRef  MathSciNet  MATH  Google Scholar 

  13. A. Gardiner, Arc transitivity in graphs II, Quart. J. Math. (Oxford) (2) 25 (1974), 163–167.

    CrossRef  MathSciNet  MATH  Google Scholar 

  14. A. Gardiner, Arc transitivity in graphs III, Quart. J. Math. (Oxford) (2) 27 (1976), 313–323.

    CrossRef  MathSciNet  MATH  Google Scholar 

  15. A. Gardiner, Doubly primitive vertex stabilisers in graphs, Math. Z. 135 (1974) 157–166.

    CrossRef  MathSciNet  MATH  Google Scholar 

  16. A. Gardiner, Antipodal covering graphs, J. Combinatorial Theory (B) 16 (1974), 255–273.

    CrossRef  MathSciNet  MATH  Google Scholar 

  17. A. Gardiner, Imprimitive distance-regular graphs and projective planes, J. Combinatorial Theory (B) 16 (1974), 274–281.

    CrossRef  MathSciNet  MATH  Google Scholar 

  18. T.G. Ostrom and A. Wagner, On projective and affine planes with transitive collineation groups, Math. Z. 71 (1959), 186–199.

    CrossRef  MathSciNet  MATH  Google Scholar 

  19. C.E. Praeger, Graphs and their automorphism groups, in Proc. 1st Western Australian Algebra Conference (ed. P. Schultz, C.E. Praeger, R.P. Sullivan), Dekker, 1981, to appear.

    Google Scholar 

  20. C.E. Praeger, Symmetric graphs and a characterisation of the Odd graphs, in Combinatorial Mathematics VII (ed. R.W. Robinson, G.W. Southern, W.D. Wallis), Lecture Notes in Mathematics 829, Springer, 1980, 211–219.

    Google Scholar 

  21. W.L. Quirin, Extension of some results of Manning and Wielandt on primitive permutation groups, Math. Z. 123 (1971), 223–230.

    CrossRef  MathSciNet  MATH  Google Scholar 

  22. C.C. Sims, Graphs and finite permutation groups II, Math. Z. 103 (1968), 276–281.

    CrossRef  MathSciNet  MATH  Google Scholar 

  23. D.H. Smith, Primitive and imprimitive graphs, Quart. J. Math. (Oxford) (2) 22 (1971), 551–557.

    CrossRef  MathSciNet  MATH  Google Scholar 

  24. D.H. Smith, On tetravalent graphs, J. London Math. Soc. (2) 6 (1973), 659–662.

    CrossRef  MathSciNet  MATH  Google Scholar 

  25. D.H. Smith, Distance-transitive graphs of valency four, J. London Math. Soc. (2) 8 (1974), 377–384.

    CrossRef  MathSciNet  MATH  Google Scholar 

  26. D.H. Smith, Bounding the diameter of a distance-transitive graph, J. Combinatorial Theory (B) 16 (1974), 139–144.

    CrossRef  MathSciNet  MATH  Google Scholar 

  27. D.H. Smith, On bipartite tetravalent graphs, Discrete Math. 10 (1974), 167–172.

    CrossRef  MathSciNet  MATH  Google Scholar 

  28. D.H. Smith, Highly symmetrical graphs of low valency, Ph.D. Thesis, University of Southampton, 1971.

    Google Scholar 

  29. W.T. Tutte, A family of cubical graphs, Proc. Cambridge Philos. Soc. 43 (1947), 459–474.

    CrossRef  MathSciNet  MATH  Google Scholar 

  30. R. Weiss, Groups with a (B,N)-pair and locally transitive graphs, Nagoya Math. J. 74 (1979), 1–21.

    CrossRef  MathSciNet  MATH  Google Scholar 

  31. R. Weiss, Über symmetrischen Graphen deren Valenz eine Primzahl ist, Math. Z. 136 (1974), 277–278.

    CrossRef  MathSciNet  MATH  Google Scholar 

  32. H. Whitney, Congruent graphs and connectivity of graphs, Amer. J. Math. 54 (1932), 150–168.

    CrossRef  MathSciNet  MATH  Google Scholar 

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© 1982 Springer-Verlag

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Gardiner, A. (1982). Classifying distance-transitive graphs. 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/BFb0061973

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  • DOI: https://doi.org/10.1007/BFb0061973

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