Hostname: page-component-cc8bf7c57-j4qg9 Total loading time: 0 Render date: 2024-12-11T23:03:52.189Z Has data issue: false hasContentIssue false
  • English
  • Français

Groups with a (B, N)–pair and locally transitive graphs

Published online by Cambridge University Press:  22 January 2016

Richard Weiss
Richard Weiss*
Affiliation:
II. Mathematisches Institut der Freien Universität Berlin
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Let Γ be an undirected graph and G a subgroup of aut (Γ). We denote by ∂(x, y) the distance between two vertices x and y, by E(Γ) the edge set of Γ, by V(Γ) the vertex set of Γ, by Γ(x) the set of neighbors of the vertex x and by G(x)Γ(x) the permutation group induced by the stabilizer G(x) on Γ(x).

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 74 , July 1979 , pp. 1 - 21
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1979

References

[1] Bouwer, I.Z. and Djoković, D. Ž., On regular graphs III, J. Comb. Th. B 14 (1973), 268–277.Google Scholar
[2] Carter, R. W., Simple Groups of Lie Type, John Wiley and Sons, New York, 1971.Google Scholar
[3] Feit, W. and Higman, G., The nonexistence of certain generalized polygons, J. Alg. 1 (1964), 114–131.Google Scholar
[4] Gardiner, A., Doubly primitive vertex stabilizers in graphs, Math. Z. 135 (1974), 257–266.Google Scholar
[5] Gleason, A. M., Finite Fano planes, Amer. J. Math. 78 (1956), 797–807.Google Scholar
[6] Gorenstein, D., Finite Groups, Harper and Row, New York, 1968.Google Scholar
[7] Higman, D. G., Finite permutation groups of rank 3, Math. Z. 86 (1964), 145–156.Google Scholar
[8] Knapp, W., On the point stabilizer in a primitive permutation group, Math. Z. 133 (1973), 137–168.CrossRefGoogle Scholar
[9] Tutte, W. T., A family of cubical graphs, Proc. Cambr. Phil. Soc. 43 (1947), 459–474.CrossRefGoogle Scholar
[10] Tutte, W. T., Connectivity in Graphs, University of Toronto Press, Toronto, 1966.Google Scholar
[11] Weiss, R., Über lokal s-reguläre Graphen, J. Comb. Th. B 20 (1976), 124–127.Google Scholar
[12] Yanushka, A., Generalized hexagons of order (t, t), Israel J. Math. 23 (1976), 309–324.CrossRefGoogle Scholar