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In an integral domain R, the decomposition of a nonzero noninvertible element a as a product of prime (or irreducible) factors a=p_1...p_n, (1) is unique if every other ...

Let the vertices of a graph G be numbered with distinct integers 1 to |G|. Then the dilation of G is the maximum (absolute) difference between integers assigned to adjacent ...

The prime distance pd(n) of a nonnegative integer n is the absolute difference between n and the nearest prime. It is therefore true that pd(p)=0 for primes p. The first few ...

The problem of packing a set of items into a number of bins such that the total weight, volume, etc. does not exceed some maximum value. A simple algorithm (the first-fit ...

The (weak) Bruhat graph B_n of order n is the simple graph having have all permutations of {1,2,...,n} as vertices, and with an edge between pairs of permutations that differ ...

The chromatic polynomial pi_G(z) of an undirected graph G, also denoted C(G;z) (Biggs 1973, p. 106) and P(G,x) (Godsil and Royle 2001, p. 358), is a polynomial which encodes ...

A nonplanar graph G is said to be critical nonplanar if the removal of a vertex results in a planar graph for every vertex of G. Critical nonplanar graphs differ from apex ...

The Fibonacci cube graph of order n is a graph on F_(n+2) vertices, where F_n is a Fibonacci number, labeled by the Zeckendorf representations of the numbers 0 to F_(n+2)-1 ...

Turing machines are defined by sets of rules that operate on four parameters: (state, tape cell color, operation, state). Let the states and tape cell colors be numbered and ...

There are a number of tilings of various shapes by all the 12 order n=6 polyiamonds, summarized in the following table. Several of these (starred in the table below) are also ...