Hostname: page-component-6d856f89d9-5pczc Total loading time: 0 Render date: 2024-07-16T07:35:54.316Z Has data issue: false hasContentIssue false
  • English
  • Français

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.
Get access Rights & Permissions [Opens in a new window]

Extract

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.

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

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