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A graph G is Hamilton-connected if every two vertices of G are connected by a Hamiltonian path (Bondy and Murty 1976, p. 61). In other words, a graph is Hamilton-connected if ...

An inner product is a generalization of the dot product. In a vector space, it is a way to multiply vectors together, with the result of this multiplication being a scalar. ...

A Moore graph of type (v,g) is a regular graph of vertex degree v>2 and girth g that contains the maximum possible number of nodes, namely ...

Orthogonal polynomials are classes of polynomials {p_n(x)} defined over a range [a,b] that obey an orthogonality relation int_a^bw(x)p_m(x)p_n(x)dx=delta_(mn)c_n, (1) where ...

A game played on a board of a given shape consisting of a number of holes of which all but one are initially filled with pegs. The goal is to remove all pegs but one by ...

A complete oriented graph (Skiena 1990, p. 175), i.e., a graph in which every pair of nodes is connected by a single uniquely directed edge. The first and second 3-node ...

The tribonacci numbers are a generalization of the Fibonacci numbers defined by T_1=1, T_2=1, T_3=2, and the recurrence equation T_n=T_(n-1)+T_(n-2)+T_(n-3) (1) for n>=4 ...

The wreath graph W(n,k) is the graph obtained by taking n collections of k nodes and arranging around a circle such that all nodes in adjacent collections are connected. ...

The number 10 (ten) is the basis for the decimal system of notation. In this system, each "decimal place" consists of a digit 0-9 arranged such that each digit is multiplied ...

A real number that is b-normal for every base 2, 3, 4, ... is said to be absolutely normal. As proved by Borel (1922, p. 198), almost all real numbers in [0,1) are absolutely ...