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Zamfirescu Graphs

ZamfirescuGraphs

There are a number of graphs associated with T. I. (and C. T.) Zamfirescu. The Zamfirescu graphs on 36 and 75 vertices, the former of which is a snark, appear in Zamfirescu (1976). The Zamfirescu graph on 48 vertices appears in Zamfirescu and Zamfirescu (2007) and is a planar hypohamiltonian graph.

The Zamfirescu graphs are implemented in the Wolfram Language as GraphData["ZamfirescuGraph36"], GraphData["ZamfirescuGraph48"], and GraphData["ZamfirescuGraph75"], respectively.

ZamfirescuGraphMatrices

The figures above show the adjacency, incidence, and graph distance matrices of the Zamfirescu 48-graph.

See also

Hatzel Graph, Hypohamiltonian Graph, Hypotraceable Graph, Planar Hypohamiltonian Graph, Wiener-Araya Graph

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References

Zamfirescu, T. "On Longest Paths and Circuits in Graphs." Math. Scand. 38, 211-239, 1976.Zamfirescu, C. T. and Zamfirescu, T. I. "A Planar Hypohamiltonian Graph with 48 Vertices." J. Graph Th. 48, 338-342, 2007.

Cite this as:

Weisstein, Eric W. "Zamfirescu Graphs." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/ZamfirescuGraphs.html

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