Hostname: page-component-586b7cd67f-g8jcs Total loading time: 0 Render date: 2024-12-02T19:55:35.556Z Has data issue: false hasContentIssue false
  • English
  • Français

A Minimal Cubic Graph of Girth Seven

Published online by Cambridge University Press:  20 November 2018

W. F. McGee
W. F. McGee*
Affiliation:
University of Toronto
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

A “cubic” graph is one with three edges incident on each vertex. Let v and e be the number of vertices and edges, respectively. Then 3v = 2e for a cubic graph. The girth of a graph is the smallest number of edges in any non-trivial polygon. A minimal graph is one with the smallest number of edges with its particular properties. The minimal cubic graphs of girths one to eight, excluding seven, are discussed in Tutte's paper [1]. A minimal cubic graph of girth seven is given here.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 3 , Issue 2 , 01 May 1960 , pp. 149 - 152
Copyright
Copyright © Canadian Mathematical Society 1960

References

1. Tutte, W. T., A family of cubical graphs, Proc. Cambridge. Philos. Soc. 43 (1947), 459-474.Google Scholar
2. Tutte, W. T., A non-Hamiltonian graph, Canad. Math. Bull.3 (1960), 1-5.Google Scholar
3. Coxeter, H. S. M., Self-dual configurations and regular graphs, Bull. Amer. Math. Soc. 56 (1950), 413-455.Google Scholar