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A complete graph is a graph in which each pair of graph vertices is connected by an edge. The complete graph with n graph vertices is denoted K_n and has (n; 2)=n(n-1)/2 (the ...

Given an undirected graph, a degree sequence is a monotonic nonincreasing sequence of the vertex degrees (valencies) of its graph vertices. The number of degree sequences for ...

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 ...

A k-regular simple graph G on nu nodes is strongly k-regular if there exist positive integers k, lambda, and mu such that every vertex has k neighbors (i.e., the graph is a ...

The (small) rhombicosidodecahedron (Cundy and Rowlett 1989, p. 111), sometimes simply called the rhombicosidodecahedron (Maeder 1997; Wenninger 1989, p. 27; Conway et al. ...

A polygonal number of the form O_n=n(3n-2). The first few are 1, 8, 21, 40, 65, 96, 133, 176, ... (OEIS A000567). The generating function for the octagonal numbers is ...

A deltahedron is a polyhedron whose faces are congruent equilateral triangles (Wells 1986, p. 73). Note that polyhedra whose faces could be triangulated so as to be composed ...

Augmentation is the dual operation of truncation which replaces the faces of a polyhedron with pyramids of height h (where h may be positive, zero, or negative) having the ...

A dipyramid, also called a bipyramid, consists of two pyramids symmetrically placed base-to-base. The dipyramids are duals of the regular prisms. Their skeletons are the ...

A polyhedron dissection (or decomposition) is a dissection of one or more polyhedra into other shapes. Two polyhedra can be dissected into each other iff they have equal Dehn ...