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The complete elliptic integral of the second kind, illustrated above as a function of k, is defined by E(k) = E(1/2pi,k) (1) = ...

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 ...

Assignment of each graph edge of a graph to one of two color classes (commonly designation "red" and "green").

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"].

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).