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A planar graph G is said to be triangulated (also called maximal planar) if the addition of any edge to G results in a nonplanar graph. If the special cases of the triangle ...

A block graph, also called a clique tree, is a simple graph in which every block is a complete graph. The numbers of connected block graphs on n=1, 2, ... vertices are 1, 1, ...

The rhombicosahedral graph, illustrated above, is the skeleton of the icosidodecadodecahedron, rhombicosahedron and rhombidodecadodecahedron. It will be implemented in a ...

The Nechushtan graph, illustrated above, is a 10-vertex 5-chromatic graph that is unit-distance in 3 dimensions. It was used by Nechushtan (2002) in the construction of of a ...

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 rising sun graph is the graph on 7 vertices illustrated above. It is implemented in the Wolfram Language as GraphData["RisingSunGraph"].

A chordal graph is a simple graph in which every graph cycle of length four and greater has a cycle chord. In other words, a chordal graph is a graph possessing no chordless ...

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"].

A planar graph corresponding to polyhedra skeletons. The polyhedral graphs are special cases.

A graph G is k-factorable if it is the union of disjoint k-factors (Skiena 1990, p. 244).