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For a given positive integer n, does there exist a weighted tree with n graph vertices whose paths have weights 1, 2, ..., (n; 2), where (n; 2) is a binomial coefficient? ...

The tetragonal antiwedge is the topological class of hexahedron. It has 10 edges and 6 vertices and its faces consist of 4 triangles and 2 quadrilaterals. A tetragonal ...

A planar graph G is said to be triangulated (also called maximal planar) if the addition of any edge to G results in a nonplanar graph. If the special cases of the triangle ...

In 1704, Sebastien Truchet considered all possible patterns formed by tilings of right triangles oriented at the four corners of a square (Wolfram 2002, p. 875). Truchet's ...

The truncated great dodecahedron is the uniform polyhedron with Maeder index 37 (Maeder 1997), Wenninger index 75 (Wenninger 1989), Coxeter index 47 (Coxeter et al. 1954), ...

A uniform distribution, sometimes also known as a rectangular distribution, is a distribution that has constant probability. The probability density function and cumulative ...

A unimodular matrix is a real square matrix A with determinant det(A)=+/-1 (Born and Wolf 1980, p. 55; Goldstein 1980, p. 149). More generally, a matrix A with elements in ...

A vertex cut, also called a vertex cut set or separating set (West 2000, p. 148), of a connected graph G is a subset of the vertex set S subset= V(G) such that G-S has more ...

The degree of a graph vertex v of a graph G is the number of graph edges which touch v. The vertex degrees are illustrated above for a random graph. The vertex degree is also ...

The game of billiards is played on a rectangular table (known as a billiard table) upon which balls are placed. One ball (the "cue ball") is then struck with the end of a ...