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A cusp catastrophe is a catastrophe which can occur for two control factors and one behavior axis. The cusp catastrophe is the universal unfolding of the singularity f(x)=x^4 ...

There are four strongly regular graphs with parameters (nu,k,lambda,mu)=(28,12,6,4), one of them being the triangular graph of order 8. The other three such graphs are known ...

An error-correcting code is an algorithm for expressing a sequence of numbers such that any errors which are introduced can be detected and corrected (within certain ...

The Gray graph is a cubic semisymmetric graph on 54 vertices. It was discovered by Marion C. Gray in 1932, and was first published by Bouwer (1968). Malnič et al. (2002) ...

A Lucas cube graph of order n is a graph that can be defined based on the n-Fibonacci cube graph by forbidding vertex strings that have a 1 both in the first and last ...

The Meringer graph is one of the four (5,5)-cage graphs, discovered by Meringer (1999) after it had long been thought that only three such cages existed. Like the other ...

Assume that n numbered pancakes are stacked, and that a spatula can be used to reverse the order of the top k pancakes for 2<=k<=n. Then the pancake sorting problem asks how ...

The factorization of a number into its constituent primes, also called prime decomposition. Given a positive integer n>=2, the prime factorization is written ...

A knot is called prime if, for any decomposition as a connected sum, one of the factors is unknotted (Livingston 1993, pp. 5 and 78). A knot which is not prime is called a ...

The Sierpiński gasket graph of order n is the graph obtained from the connectivity of the Sierpiński sieve. The first few Sierpiński gasket graphs are illustrated above. S_2 ...