Search Results for ""

The Paley graph of order q with q a prime power is a graph on q nodes with two nodes adjacent if their difference is a square in the finite field GF(q). This graph is ...

The Pappus graph is a cubic symmetric distance-regular graph on 18 vertices, illustrated above in three embeddings. It is Hamiltonian and can be represented in LCF notation ...

If there is an integer 0<x<p such that x^2=q (mod p), (1) i.e., the congruence (1) has a solution, then q is said to be a quadratic residue (mod p). Note that the trivial ...

What is the maximum number of queens that can be placed on an n×n chessboard such that no two attack one another? The answer is n-1 queens for n=2 or n=3 and n queens ...

A regular polygon is an n-sided polygon in which the sides are all the same length and are symmetrically placed about a common center (i.e., the polygon is both equiangular ...

Sylvester's four-point problem asks for the probability q(R) that four points chosen at random in a planar region R have a convex hull which is a quadrilateral (Sylvester ...

In his Meditationes algebraicae, Waring (1770, 1782) proposed a generalization of Lagrange's four-square theorem, stating that every rational integer is the sum of a fixed ...

Just as many interesting integer sequences can be defined and their properties studied, it is often of interest to additionally determine which of their elements are prime. ...

The divisor function sigma_k(n) for n an integer is defined as the sum of the kth powers of the (positive integer) divisors of n, sigma_k(n)=sum_(d|n)d^k. (1) It is ...

The dodecahedral graph is the Platonic graph corresponding to the connectivity of the vertices of a dodecahedron, illustrated above in four embeddings. The left embedding ...