Advertisement

Triangles in labelled cubic graphs

  • N. C. Wormald
Contributed Papers
Part of the Lecture Notes in Mathematics book series (LNM, volume 686)

Abstract

No cubic graph has an odd number of points. A method is found of calculating the number tp of labelled connected cubic graphs with 2p points rooted at a triangle. The method presupposes knowledge of the numbers qk of labelled connected cubic graphs with 2k points and k<p. Labelled connected cubic graphs have already been counted by Read, so this allows determination of the mean number tp/qp of triangles in a labelled connected cubic graph with 2p points, for all p>1. It is shown that tp/qp → 4/3 as p → ∞.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    F. Harary, The number of dissimilar supergraphs of a linear graph, Pacific J. Math. 7 (1957) 903–911.MathSciNetCrossRefMATHGoogle Scholar
  2. [2]
    F. Harary, Graph Theory. Addison-Wesley, Reading, Mass., 1969.MATHGoogle Scholar
  3. [3]
    F. Harary and E.M. Palmer, Graphical Enumeration. Academic Press, New York, 1973.MATHGoogle Scholar
  4. [4]
    R.C. Read, The enumeration of locally restricted graphs II, J. London Math. Soc. 35 (1960) 344–351.MathSciNetCrossRefMATHGoogle Scholar
  5. [5]
    R.C. Read, Some unusual enumeration problems, Annals N.Y. Acad. Sci. 175 (1970) 314–326.MathSciNetCrossRefMATHGoogle Scholar
  6. [6]
    R.W. Robinson, Enumeration of colored graphs, J. Combinatorial Theory 4 (1968) 181–190.MathSciNetCrossRefMATHGoogle Scholar
  7. [7]
    N. Wormald, Enumeration of labelled graphs II: Cubic graphs with a given connectedness, to appear.Google Scholar

Copyright information

© Springer-Verlag 1978

Authors and Affiliations

  • N. C. Wormald
    • 1
  1. 1.Department of MathematicsUniversity of NewcastleAustralia

Personalised recommendations