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A tree with its nodes labeled. The number of labeled trees on n nodes is n^(n-2), the first few values of which are 1, 1, 3, 16, 125, 1296, ... (OEIS A000272). Cayley (1889) ...

A game in which each player has a finite number of moves and a finite number of choices at each move.

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 ...

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

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

A dozen dozen, or the square number 144.

Schubert's application of the conservation of number principle.

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

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, ...

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