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Planar and outerplanar cayley graphs of free groups

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Theory and Applications of Graphs

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 642))

Abstract

All finite planar graphs are subgraphs of certain planar Cayley graphs of free groups; outerplanar graphs are subgraphs of certain outerplanar Cayley graphs of free groups. It is shown for these particular planar presentations of free groups that special planar is equivalent with outerplanar.

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References

  1. J. Battle, F. Harary, Y. Kodama and J.W.T. Youngs, Additivity of the genus of a graph, Bull. Amer. Math. Soc. 68, (1962), 565–568.

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  2. H. Levinson, On the genera of graphs of group presentations, Ann. N. Y. Acad. Sci. 175, Art. 1, (1970), 277–284.

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  3. H. Levinson, On the genera of graphs of group presentations III, J. Comb. Theory,Series B 13, (1972), 298–302.

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  4. H. Levinson and E. S. Rapaport, Planarity of Cayley diagrams, Graph Theory and Applications. Springer-Verlag, Berlin (1972), 183–188.

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  5. C. W. Marshall, Applied Graph Theory. Wiley-Interscience, New York (1971).

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  6. E. R. Strasser and H. Levinson, Planarity of Cayley diagrams: planar presentations, Proc. 6th S-E Conf. Combinatorics, Graph Theory, and Computing. Utilitas Mathematica, Winnipeg (1975), 567–593.

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Author information

Authors and Affiliations

  1. Rutgers University, New Brunswick, N. J., 08903, USA

    H. W. Levinson

Authors
  1. H. W. Levinson
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Editor information

Editors and Affiliations

  1. Department of Mathematics, Western Michigan University, Kalamazoo, MI, 49008, USA

    Yousef Alavi  & Don R. Lick  & 

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© 1978 Springer-Verlag Berlin Heidelberg

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Levinson, H.W. (1978). Planar and outerplanar cayley graphs of free groups. In: Alavi, Y., Lick, D.R. (eds) Theory and Applications of Graphs. Lecture Notes in Mathematics, vol 642. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0070390

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  • DOI: https://doi.org/10.1007/BFb0070390

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-08666-6

  • Online ISBN: 978-3-540-35912-8

  • eBook Packages: Springer Book Archive

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