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The smallest possible number of vertices a polyhedral nonhamiltonian graph can have is 11, and there exist 74 such graphs. The Goldner-Harary graph (Goldner and Harary 1975a, ...

The term "integral" can refer to a number of different concepts in mathematics. The most common meaning is the the fundamenetal object of calculus corresponding to summing ...

A perfect magic cube is a magic cube for which the rows, columns, pillars, space diagonals, and diagonals of each n×n orthogonal slice sum to the same number (i.e., the magic ...

A square which can be dissected into a number of smaller squares with no two equal is called a perfect square dissection (or a squared square). Square dissections in which ...

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 graph G having chromatic number chi(G)<=k is called a k-colorable graph (Harary 1994, p. 127). In contrast, a graph having chi(G)=k is said to be a k-chromatic graph. Note ...

For P, Q, R, and S polynomials in n variables [P·Q,R·S]=sum_(i_1,...,i_n>=0)A/(i_1!...i_n!), (1) where A=[R^((i_1,...,i_n))(D_1,...,D_n)Q(x_1,...,x_n) ...

Cahen's constant is defined as C = sum_(k=0)^(infty)((-1)^k)/(a_k-1) (1) = 0.64341054628... (2) (OEIS A118227), where a_k is the kth term of Sylvester's sequence.

The conjecture made by Belgian mathematician Eugène Charles Catalan in 1844 that 8 and 9 (2^3 and 3^2) are the only consecutive powers (excluding 0 and 1). In other words, ...

The inequality (j+1)a_j+a_i>=(j+1)i, which is satisfied by all A-sequences.