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The Steiner tree of some subset of the vertices of a graph G is a minimum-weight connected subgraph of G that includes all the vertices. It is always a tree. Steiner trees ...

Combinatorial geometry is a blending of principles from the areas of combinatorics and geometry. It deals with combinations and arrangements of geometric objects and with ...

Combinatorics is the branch of mathematics studying the enumeration, combination, and permutation of sets of elements and the mathematical relations that characterize their ...

A d-dimensional discrete percolation model is said to be inhomogeneous if different graph edges (in the case of bond percolation models) or vertices (in the case of site ...

A state diagram is a labeled directed graph together with state information that can be used to indicate that certain paths on in a system may be traversed only in a certain ...

The shortest circular sequence of length sigma^n such that every string of length n on the alphabet a of size sigma occurs as a contiguous subrange of the sequence described ...

A hexahedron is a polyhedron with six faces. The figure above shows a number of named hexahedra, in particular the acute golden rhombohedron, cube, cuboid, hemicube, ...

Combinatorial matrix theory is a rich branch of mathematics that combines combinatorics, graph theory, and linear algebra. It includes the theory of matrices with prescribed ...

C_7 is the cyclic group that is the unique group of group order 7. Examples include the point group C_7 and the integers modulo 7 under addition (Z_7). No modulo ...

The Goddard-Henning enneahedron, a term coined here, is the canonical polyhedron obtained from the Goddard-Henning graph. It has 9 vertices, 16 edges (consisting of 3 ...