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A graph G is the edge graph of a polyhedron iff G is a simple planar graph which is 3-connected.

The set of all centroid points in a weighted tree (Harary 1994, p. 36).

A k-factor of a graph is a k-regular subgraph of order n. k-factors are a generalization of complete matchings. A perfect matching is a 1-factor (Skiena 1990, p. 244).

An object created by folding a piece of paper along certain lines to form loops. The number of states possible in an n-flexagon is a Catalan number. By manipulating the ...

A parallelogram polyomino is a polyomino such that the intersection with every line perpendicular to the main diagonal is a connected segment. The number of parallelogram ...

The chromatic invariant theta(G) of a connected graph G is the number of spanning trees of G that have internal activity 1 and external activity 0. For graphs other than the ...

A simple graph, also called a strict graph (Tutte 1998, p. 2), is an unweighted, undirected graph containing no graph loops or multiple edges (Gibbons 1985, p. 2; West 2000, ...

The Carlson elliptic integrals, also known as the Carlson symmetric forms, are a standard set of canonical elliptic integrals which provide a convenient alternative to ...

Given an m×n matrix A, the fundamental theorem of linear algebra is a collection of results relating various properties of the four fundamental matrix subspaces of A. In ...

The term "pathological" is used in mathematics to refer to an example specifically cooked up to violate certain almost universally valid properties. Pathological problems ...