TOPICS
Zamfirescu Graphs
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.
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 GraphExplore with Wolfram|Alpha
References
House of Graphs. Zamfirescu Graphs. Zamfirescu Graph 36, Zamfirescu Graph 48, and Zamfirescu Graph 75.Zamfirescu, C. T. and Zamfirescu, T. I. "A Planar Hypohamiltonian Graph with 48 Vertices." J. Graph Th. 48, 338-342, 2007.Zamfirescu, T. "On Longest Paths and Circuits in Graphs." Math. Scand. 38, 211-239, 1976.Referenced on Wolfram|Alpha
Zamfirescu GraphsCite this as:
Weisstein, Eric W. "Zamfirescu Graphs." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/ZamfirescuGraphs.html