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The uniformity conjecture postulates a relationship between the syntactic length of expressions built up from the natural numbers using field operations, exponentials, and ...

The number of nodes in a graph is called its order.

An unknot which can only be unknotted by first increasing the number of crossings.

The operation of taking an nth root of a number.

B_(p+k)=B_k+B_(k+1) (mod p), when p is prime and B_n is a Bell number.

A graph is planar if it can be drawn in a plane without graph edges crossing (i.e., it has graph crossing number 0). The number of planar graphs with n=1, 2, ... nodes are 1, ...

An Ore graph is a graph that satisfies Ore's theorem, i.e., a graph G for which the sums of the degrees of nonadjacent vertices is greater than or equal to the number of ...

The co-rank of a graph G is defined as s(G)=m-n+c, where m is the number of edges of G, n is the number of vertices, and c is the number of connected components (Biggs 1993, ...

In any tree, the number of dissimilar points minus the number of dissimilar lines plus the number of symmetry lines equals 1.

A Wagstaff prime is a prime number of the form (2^p+1)/3 for p a prime number. The first few are given by p=3, 5, 7, 11, 13, 17, 19, 23, 31, 43, 61, 79, 101, 127, 167, 191, ...