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A spanning tree of a graph on n vertices is a subset of n-1 edges that form a tree (Skiena 1990, p. 227). For example, the spanning trees of the cycle graph C_4, diamond ...

A number of attractive tetrahedron 6-compounds can be constructed. The first compound (left figures) is obtained by combining three stella octangula. A second can be obtained ...

A truncated polyhedron is a polyhedron with truncated faces, given by the Schläfli symbol t{p; q}. The operation implemented as Truncate[polyhedron, r] in the Wolfram ...

The n-wheel complement graph W^__n is the graph complement of the n-wheel graph. For n>4, W^__n is isomorphic to the graph disjoint union of a circulant graph ...

Define the packing density eta of a packing of spheres to be the fraction of a volume filled by the spheres. In three dimensions, there are three periodic packings for ...

Clean tile is a game investigated by Buffon (1777) in which players bet on the number of different tiles a thrown coin will partially cover on a floor that is regularly ...

There are a number of attractive polyhedron compounds of two cubes. The first (left figures) is obtained by allowing two cubes to share opposite polyhedron vertices then ...

The quantities obtained from cubic, hexagonal, etc., lattice sums, evaluated at s=1, are called Madelung constants. For cubic lattice sums ...

The concept of "random close packing" was shown by Torquato et al. (2000) to be mathematically ill-defined idea that is better replaced by the notion of "maximally random ...

The gear graph, also sometimes known as a bipartite wheel graph (Brandstädt et al. 1987), is a wheel graph with a graph vertex added between each pair of adjacent graph ...