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The Chords of the Non-Ruled Quadric In PG(3, 3)

Published online by Cambridge University Press:  20 November 2018

W. T. Tutte
W. T. Tutte*
Affiliation:
University of Toronto
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The 8-cage (3) may be defined as the simplest cubic graph having no circuit of fewer than eight edges. To construct it we first observe that it must contain a tree T whose vertices are of degrees 1 and 3 and in which each vertex of degree 1 is separated by an arc of just three edges from a central edge AB. These properties fix the structure of T uniquely.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 10 , 1958 , pp. 481 - 483
Copyright
Copyright © Canadian Mathematical Society 1958

References

1. Coxeter, H. S. M., Self-dual configurations and regular graphs, Bull. Amer. Math. Soc, 56 (1950), 413-455.Google Scholar
2. Edge, W. L., Geometry in three dimensions over GF(3), Proc. Roy. Soc. 222 (1953), 262-286.Google Scholar
3. Tutte, W. T., A family of cubical graphs, Proc. Cambridge Philos. Soc, 4-3 (1947), 459-474.Google Scholar