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Let h be the number of sides of certain skew polygons (Coxeter 1973, p. 15). Then h=(2(p+q+2))/(10-p-q).

The smallest cubic graphs with graph crossing number CN(G)=n have been termed "crossing number graphs" or n-crossing graphs by Pegg and Exoo (2009). The n-crossing graphs are ...

In a network with three graph edges at each graph vertex, the number of Hamiltonian cycles through a specified graph edge is 0 or even.

A symmetric design is a block design (v, k, lambda, r, b) with the same number of blocks as points, so b=v (or, equivalently, r=k). An example of a symmetric block design is ...

The Szekeres snark was the fifth snark discovered, illustrated above. It has 50 vertices and edge chromatic number 4.

The number of graph edges meeting at a given node in a graph is called the order of that graph vertex.

x^n=sum_(k=0)^n<n; k>(x+k; n), where <n; k> is an Eulerian number and (n; k) is a binomial coefficient (Worpitzky 1883; Comtet 1974, p. 242).

A general quadratic Diophantine equation in two variables x and y is given by ax^2+cy^2=k, (1) where a, c, and k are specified (positive or negative) integers and x and y are ...

Apéry's constant is defined by zeta(3)=1.2020569..., (1) (OEIS A002117) where zeta(z) is the Riemann zeta function. B. Haible and T. Papanikolaou computed zeta(3) to 1000000 ...

An out-shuffle, also known as a perfect shuffle (Golomb 1961), is a riffle shuffle in which the top half of the deck is placed in the right hand, and cards are then ...