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A useful family of bicubic graphs

Part III: Contributed Papers New Results On Graphs And Combinatorics

Part of the Lecture Notes in Mathematics book series (LNM,volume 406)

Abstract

Let the vertices of a 2n-gon be labelled, in an order of traversal: 0, 1′, 1, 2′, 2, ..., (n−1)′, n−1, 0′. Let G(n,m) denote the bicubic graph derived from this 2n-gon by adjunction of the chords (i,(i+m)′), i = 0, 1, 2, ..., n−1, the addition being taken modulo n. Restricting ourselves to the case when n is prime, we determine the isomorphism classes of the graphs G(n,m), and the corresponding automorphism groups. Various applications are discussed.

Keywords

  • Automorphism Group
  • Regular Graph
  • Isomorphism Class
  • Dihedral Group
  • Regular Representation

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. Bouwer, I. Z., and Frucht, R., "Line Minimal Graphs with Cyclic Groups," A Survey of Combinatorial Theory, (Ed. J. N. Srivastava), North-Holland, New York, 1973, 53–67.

    Google Scholar 

  2. Coxeter, H. S. M., "Self-dual Configurations and Regular Graphs," Bull. Amer. Math. Soc. 56 (1950), 413–455.

    CrossRef  MathSciNet  MATH  Google Scholar 

  3. Coxeter, H. S. M. and Moser, W. O. J., "Generators and Relations for Discrete Groups," 3rd Edition, Springer-Verlag, New York, 1972, Section 8.4, 107–109.

    CrossRef  MATH  Google Scholar 

  4. Foster, R. M., "A Census of Trivalent Symmetrical Graphs I," presented at the conference on Graph Theory and Combin. Analysis, Waterloo, Ontario, 1966.

    Google Scholar 

  5. Frucht, R., "A One-regular Graph of Degree Three," Canad. J. Math. 4 (1952), 240–247.

    CrossRef  MathSciNet  MATH  Google Scholar 

  6. Frucht, R., "How to Describe a Graph," Ann. N. Y. Ac. Sci. 175, Part I (1970), 159–167.

    MathSciNet  MATH  Google Scholar 

  7. Harary, F., "Graph Theory," Addison-Wesley, Reading, Mass., 1969.

    Google Scholar 

  8. Miller, R. C., "The Trivalent Symmetric Graphs of Girth at Most 6", J. Combinatorial Theory, Series B, 10 (1971), 163–182.

    CrossRef  MATH  Google Scholar 

  9. Tutte, W. T., "A Family of Cubical Graphs," Proc. Cambridge Philos. Soc. 43 (1947), 459–474.

    CrossRef  MathSciNet  MATH  Google Scholar 

  10. Watkins, M. E., "On the Action of Non-abelian Groups on Graphs," J. Combinatorial Theory 11 (1971), 95–104.

    CrossRef  MathSciNet  MATH  Google Scholar 

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© 1974 Springer-Verlag Berlin

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Boreham, T.G., Bouwer, I.Z., Frucht, R.W. (1974). A useful family of bicubic graphs. In: Bari, R.A., Harary, F. (eds) Graphs and Combinatorics. Lecture Notes in Mathematics, vol 406. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0066443

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  • DOI: https://doi.org/10.1007/BFb0066443

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-06854-9

  • Online ISBN: 978-3-540-37809-9

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