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Triangles in labelled cubic graphs

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Combinatorial Mathematics

Part of the book series: Lecture Notes in Mathematics ((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 → ∞.

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References

  1. F. Harary, The number of dissimilar supergraphs of a linear graph, Pacific J. Math. 7 (1957) 903–911.

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Author information

Authors and Affiliations

  1. Department of Mathematics, University of Newcastle, 2308, New South Wales, Australia

    N. C. Wormald

Authors
  1. N. C. Wormald
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D. A. Holton Jennifer Seberry

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© 1978 Springer-Verlag

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Wormald, N.C. (1978). Triangles in labelled cubic graphs. In: Holton, D.A., Seberry, J. (eds) Combinatorial Mathematics. Lecture Notes in Mathematics, vol 686. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0062550

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  • DOI: https://doi.org/10.1007/BFb0062550

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-08953-7

  • Online ISBN: 978-3-540-35702-5

  • eBook Packages: Springer Book Archive

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