Owens Graphs


A number of graphs are associated with P. J. Owens.

The 76-node Owens graph (Owens 1980) provides the smallest known example of a polyhedral quintic nonhamiltonian graph. It was constructed by inserting copies of the skeleton of the gyroelongated pentagonal pyramid J_(11) at the 10 of the 11 vertices of the Herschel graph.

The 78-node Owens graph (Owens 1983) is a bicubic nonhamiltonian graph which at the time was the smallest such graph known. It was constructed by various operations on the generalized Petersen graph GP(8,2).

These former of these graphs is implemented in the Wolfram Language as GraphData["OwensGraph76"].

See also

Bicubic Nonhamiltonian Graph, Quintic Nonhamiltonian Graph

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Owens, P. J. "On Regular Graphs and Hamiltonian Circuits, Including Answers to Some Questions of Joseph Zaks." J. Combin. Theory, Ser. B 28, 262-277, 1980.Owens, P. J. "Bipartite Cubic Graphs and a Shortness Exponent." Disc. Math. 44, 327-330, 1983.

Cite this as:

Weisstein, Eric W. "Owens Graphs." From MathWorld--A Wolfram Web Resource.

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