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Presentations for (G, s)-transitive graphs of small valency

Published online by Cambridge University Press:  24 October 2008

Richard Weiss
Richard Weiss
Affiliation:
Department of Mathematics, Tufts University, Medford, MA 02155, U.S.A.
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Given a group G, a subgroup H and an element a ∈ G, we define Γ(G, H, a) to be the graph on the set of left-cosets of H in G, where two left-cosets g1H and g2H are adjacent whenever . We will consider this construction only in the case that

The first of these conditions assures that adjacency is a symmetric relation (i.e. that Γ(G, H, a) is an undirected graph) and the second assures that Γ(G, H, a) is connected.

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Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 101 , Issue 1 , January 1987 , pp. 7 - 20
Copyright
Copyright © Cambridge Philosophical Society 1987

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References

REFERENCES

[1]Biggs., N. L. Presentations for cubic graphs, in Computational Group Theory, ed. Atkinson, M. D. (Academic Press, 1984), pp. 57–63.Google Scholar
[2]Biggs., N. L.Homological coverings of graphs. J. London Math. Soc. 30 (1984), 1–14.Google Scholar
[3]Biggs, N. L. and Hoare., M. J.The sextet construction for cubic graphs. Combinatorica 3 (1983), 153–165.Google Scholar
[4]Djokovic, D. Z. and Miller., G. L.Regular groups of automorphisms of cubic graphs. J. Combin. Theory Ser. B 29 (1980), 195–230.CrossRefGoogle Scholar
[5]Feit, W. and Higman., G.The nonexistence of certain generalized polygons. J. Algebra 1 (1964), 114–131.Google Scholar
[6]Fong, P. and Seitz., G. M.Groups with a (B, N)-pair of rank 2, I-II. Invent. Math. 21 (1973), and 24 (1974), 191–239.CrossRefGoogle Scholar
[7]Miller., R. C.The trivalent symmetric graphs of girth at most six. J. Combin. Theory 10 (1971), 163–182.Google Scholar
[8]Suzuki., M.Transitive extensions of a class of doubly transitive groups. Nagoya Math. J. 27 (1966), 159–169.Google Scholar
[9]Tits., J.Sur la trialité et certains groupes qui s'en déduisent. Publ. Math. I.H.E.S. 2 (1959), 37–60.CrossRefGoogle Scholar
[10]Tutte., W. T.Connectivity in Graphs (University of Toronto Press, 1966).Google Scholar
[11]Weiss, R.. Über Tuttes Cages. Monatsh. Math. 83 (1977), 65–75.Google Scholar
[12]Weiss, R.. Groups with a (B, N)-pair and locally transitive graphs. Nagoya Math. J. 74 (1979), 1–21.Google Scholar
[13]Weiss., R.The nonexistence of 8-transitive graphs. Combinatorica 1 (1981), 309–311.Google Scholar
[14]Weiss, R.. Distance-transitive graphs and generalized polygons. Arch. Math. 45 (1985), 186–192.CrossRefGoogle Scholar
[15]Weiss, R.. A characterization and another construction of Janko's group J 3. Trans. Amer. Math. Soc. Soc. (to appear).Google Scholar
[16]Weiss, R.. A characterization of . Algebras, Groups and Geometries (to appear).Google Scholar
[17]Wong, W. J.. Determination of a class of primitive permutation groups. Math. Z. 99 (1967), 235–246.CrossRefGoogle Scholar