There are a number of graphs associated with Tudor I. Zamfirescu and his son, Carol T. Zamfirescu. The 36-vertex Zamfirescu graph is a snark in which every vertex is missed by some longest path (Zamfirescu 1976). The 48-vertex Zamfirescu graph is a planar hypohamiltonian graph (Zamfirescu and Zamfirescu 2007). The 75-vertex Zamfirescu graph is a 3-connected graph in which every pair of vertices is missed by some longest cycle (Zamfirescu 1976).
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.
