A number of interesting graphs are associated with the work of van Cleemput and Zamfirescu (2018).

Two 13- and 15-node graphs, denoted and respectively, were used in the construction of an untraceable
quintic polyhedral graph on 108 nodes which is
the smallest known such graph.

The 39-node van Cleemput-Zamfirescu graph is the smallest known (and conjectured to be smallest possible) polyhedral quartic
nonhamiltonian graph . (It is however traceable .)
The 78-node and 108-node van Cleemput-Zamfirescu graphs are the smallest known quartic and quintic graphs ,
respectively, that are untraceable and polyhedral .

These graphs are will be implemented in the Wolfram
Language as GraphData ["VanCleemputZamfirescuGraph NNN " ].

See also Nonhamiltonian Graph ,

Quartic Graph ,

Quartic
Nonhamiltonian Graph ,

Untraceable Graph
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References van Cleemput, N. and Zamfirescu, C. T. "Regular Non-Hamiltonian Polyhedral Graphs." Appl. Math. Comput. 338 192-206,
2018.
Cite this as:
Weisstein, Eric W. "van Cleemput-Zamfirescu
Graphs." From MathWorld --A Wolfram Web Resource. https://mathworld.wolfram.com/vanCleemput-ZamfirescuGraphs.html

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