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An n×n Latin square is a Latin rectangle with k=n. Specifically, a Latin square consists of n sets of the numbers 1 to n arranged in such a way that no orthogonal (row or ...

A graph G is Hamilton-connected if every two vertices of G are connected by a Hamiltonian path (Bondy and Murty 1976, p. 61). In other words, a graph is Hamilton-connected if ...

Intuitively, a model of d-dimensional percolation theory is said to be a Bernoulli model if the open/closed status of an area is completely random. In particular, it makes ...

A C-matrix is a symmetric (C^(T)=C) or antisymmetric (C^(T)=-C) C_n (-1,0,1)-matrix with diagonal elements 0 and others +/-1 that satisfies CC^(T)=(n-1)I, (1) where I is the ...

A deltahedron is a polyhedron whose faces are congruent equilateral triangles (Wells 1986, p. 73). Note that polyhedra whose faces could be triangulated so as to be composed ...

A group G is said to act on a set X when there is a map phi:G×X->X such that the following conditions hold for all elements x in X. 1. phi(e,x)=x where e is the identity ...

Intuitively, a d-dimensional discrete percolation model is said to be long-range if direct flow is possible between pairs of graph vertices or graph edges which are "very ...

In general, a singularity is a point at which an equation, surface, etc., blows up or becomes degenerate. Singularities are often also called singular points. Singularities ...

A toroidal polyhedron is a polyhedron with genus g>=1 (i.e., one having one or more holes). Examples of toroidal polyhedra include the Császár polyhedron and Szilassi ...

An untraceable graph is a graph that does not possess a Hamiltonian path, i.e., one that is not traceable. All disconnected graphs are therefore untraceable. Untraceable ...