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A polygon whose vertices are points of a point lattice. Regular lattice n-gons exists only for n=3, 4, and 6 (Schoenberg 1937, Klamkin and Chrestenson 1963, Maehara 1993). A ...

Given a map with genus g>0, Heawood showed in 1890 that the maximum number N_u of colors necessary to color a map (the chromatic number) on an unbounded surface is N_u = ...

Given a regular tetrahedron of unit volume, consider the lengths of line segments connecting pairs of points picked at random inside the tetrahedron. The distribution of ...

A fullerene is a cubic polyhedral graph having all faces 5- or 6-cycles. Examples include the 20-vertex dodecahedral graph, 24-vertex generalized Petersen graph GP(12,2), ...

An apodization function (also called a tapering function or window function) is a function used to smoothly bring a sampled signal down to zero at the edges of the sampled ...

Bonato et al. (2014, 2015) defined the burning number of a simple graph as follows. Consider a process called burning involving are discrete time steps. Each node is either ...

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 number N_d^((b))(n) of digits d in the base-b representation of a number n is called the b-ary digit count for d. The digit count is implemented in the Wolfram Language ...

All the propositions in projective geometry occur in dual pairs which have the property that, starting from either proposition of a pair, the other can be immediately ...

There are several definitions of the strength of a graph. Harary and Palmer (1959) and Harary and Palmer (1973, p. 66) define the strength of a tree as the maximum number of ...