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A One-Regular Graph of Degree Three

Published online by Cambridge University Press:  20 November 2018

Robert Frucht
Robert Frucht*
Affiliation:
Technical University “Santa Maria”, Valparaiso, Chile
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Soon after the publication of Tutte's paper [5] on m-cages, H. S. M. Coxeter asked in a letter to the author whether one-regular graphs of degree 3 exist. The purpose of the following paper is to show by an example that the answer is in the affirmative.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 4 , 1952 , pp. 240 - 247
Copyright
Copyright © Canadian Mathematical Society 1952

References

1. Coxeter, H. S. M., Self-dual configurations and regular graphs, Bull. Amer. Math. Soc, vol. 56 (1950), 413–55.Google Scholar
2. Emch, A., Triple and multiple systems, their geometric configurations and groups, Trans. Amer. Math. Soc, vol. 31 (1929), 25–42.Google Scholar
3. Foster, Ronald M., Geometrical circuits of electrical networks, Bell Telephone System, Technical Publications, Monograph B-653 (1932).Google Scholar
4. Frucht, Robert, Graphs of degree three with a given abstract group, Can. J. Math., vol. 1 (1949), 365–78.Google Scholar
5. Tutte, W. T.,A family of cubical graphs, Proc. Cambridge Phil. Soc, vol. 43 (1948), 459–74.Google Scholar