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The Wiener index W, denoted w (Wiener 1947) and also known as the "path number" or Wiener number (Plavšić et al. 1993), is a graph index defined for a graph on n nodes by ...

The binomial coefficient (n; k) is the number of ways of picking k unordered outcomes from n possibilities, also known as a combination or combinatorial number. The symbols ...

A problem posed by L. Collatz in 1937, also called the 3x+1 mapping, 3n+1 problem, Hasse's algorithm, Kakutani's problem, Syracuse algorithm, Syracuse problem, Thwaites ...

An ellipse is a curve that is the locus of all points in the plane the sum of whose distances r_1 and r_2 from two fixed points F_1 and F_2 (the foci) separated by a distance ...

A Hamiltonian cycle, also called a Hamiltonian circuit, Hamilton cycle, or Hamilton circuit, is a graph cycle (i.e., closed loop) through a graph that visits each node ...

The n-hypercube graph, also called the n-cube graph and commonly denoted Q_n or 2^n, is the graph whose vertices are the 2^k symbols epsilon_1, ..., epsilon_n where ...

The m×n knight graph is a graph on mn vertices in which each vertex represents a square in an m×n chessboard, and each edge corresponds to a legal move by a knight (which may ...

Legendre showed that there is no rational algebraic function which always gives primes. In 1752, Goldbach showed that no polynomial with integer coefficients can give a prime ...

An arithmetic progression of primes is a set of primes of the form p_1+kd for fixed p_1 and d and consecutive k, i.e., {p_1,p_1+d,p_1+2d,...}. For example, 199, 409, 619, ...

The regular tetrahedron, often simply called "the" tetrahedron, is the Platonic solid with four polyhedron vertices, six polyhedron edges, and four equivalent equilateral ...