Geodesic
A Minimal Cubic Graph of Girth Seven
Canadian mathematical bulletin, Tome 3 (1960) no. 2, pp. 149-152

Voir la notice de l'article provenant de la source Cambridge University Press

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. 
McGee, W. F. A Minimal Cubic Graph of Girth Seven. Canadian mathematical bulletin, Tome 3 (1960) no. 2, pp. 149-152. doi: 10.4153/CMB-1960-018-1
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[1] 1. Tutte, W. T., A family of cubical graphs, Proc. Cambridge. Philos. Soc. 43 (1947), 459-474. Google Scholar

[2] 2. Tutte, W. T., A non-Hamiltonian graph, Canad. Math. Bull.3 (1960), 1-5. Google Scholar

[3] 3. Coxeter, H. S. M., Self-dual configurations and regular graphs, Bull. Amer. Math. Soc. 56 (1950), 413-455. Google Scholar

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