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On the Symmetry of Cubic Graphs

Published online by Cambridge University Press:  20 November 2018

W. T. Tutte
W. T. Tutte*
Affiliation:
University of Toronto
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Let G be a connected finite graph in which each edge has two distinct ends and no two distinct edges have the same pair of ends. We suppose further that G is cubic, that is, each vertex is incident with just three edges.

An s-path in G, where s is any positive integer, is a sequence S = (v0, v1… , vs) of s + 1 vertices of G, not necessarily all distinct, which satisfies the following two conditions:

(i) Any three consecutive terms of S are distinct.

(ii) Any two consecutive terms of S are the two ends of some edge of G.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 11 , 1959 , pp. 621 - 624
Copyright
Copyright © Canadian Mathematical Society 1959

References

1. Coxeter, H. S. M., Self-dual configurations and regular graphs, Bull. Amer. Math. Soc, 56 (1950), 413–455.Google Scholar
2. Frucht, R., A one-regular graph of degree three, Can. J. Math., 4 (1952), 240–247.Google Scholar
3. Tutte, W. T., A family of cubical graphs, Proc. Camb. Phil. Soc, 43 (1948), 459–474.Google Scholar