Properties
The Coxeter graph has chromatic number 3, chromatic index 3, radius 4, diameter 4 and girth 7. It is also a 3-vertex-connected graph and a 3-edge-connected graph.
The Coxeter graph is hypohamiltonian : it does not itself have a Hamiltonian cycle but every graph formed by removing a single vertex from it is Hamiltonian. It has rectilinear crossing number 11, and is the smallest cubic graph with that crossing number currently known, but an 11-crossing, 26-vertex graph may exist (sequence A110507 in OEIS).
The Coxeter graph may be constructed from the smaller distance-regular Heawood graph by constructing a vertex for each 6-cycle in the Heawood graph and an edge for each disjoint pair of 6-cycles.
Read more about this topic: Coxeter Graph
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