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The Errera graph is the 17-node planar graph illustrated above that tangles the Kempe chains in Kempe's algorithm and thus provides an example of how Kempe's supposed proof ...

The Fritsch graph is the 9-node planar graph illustrated above that tangles the Kempe chains in Kempe's algorithm and thus provides an example of how Kempe's supposed proof ...

The great rhombicuboctahedral graph is the cubic Archimedean graph on 48 nodes and 72 edges that is the skeleton of the great rhombicuboctahedron as well as the great ...

A Hamiltonian graph, also called a Hamilton graph, is a graph possessing a Hamiltonian cycle. A graph that is not Hamiltonian is said to be nonhamiltonian. A Hamiltonian ...

The hemicubical graph is the skeleton of the hemicube. It has 7 vertices, 11 edges, and 6 faces. It is implemented in the Wolfram Language as GraphData["HemicubicalGraph"].

The hemiobelisk graph is the skeleton of the hemiobelisk. It has 7 vertices, 11 edges, and 6 faces. It is a minimal unit-distance forbidden graph. It is implemented in the ...

A quartic symmetric graph on 30 nodes and 60 edges corresponding to the skeleton of the Archimdean icosidodecahedron, great dodecahemidodecahedron, great icosidodecahedron, ...

The pentakis icosidodecahedral graph, illustrated above, is a graph on 42 vertices that is the skeleton of the pentakis icosidodecahedron.

The Soifer graph, illustrated above in a number of embeddings, is a planar graph on 9 nodes that tangles the Kempe chains in Kempe's algorithm and thus provides an example of ...

Stellation is the process of constructing polyhedra by extending the facial planes past the polyhedron edges of a given polyhedron until they intersect (Wenninger 1989). The ...