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The term "square" can be used to mean either a square number ("x^2 is the square of x") or a geometric figure consisting of a convex quadrilateral with sides of equal length ...

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 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 ...

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 trapezohedron is the dual of the square antiprism. For a square antiprism with unit edge lengths, the edge lengths of the corresponding tetragonal ...

The cubic Archimedean graph on 60 nodes and 90 edges that is the skeleton of the truncated dodecahedron. It is implemented in the Wolfram Language as ...

The truncated pentakis dodecahedron is a polyhedron on 180 vertices, 270 edges, and 92 faces. Its canonical polyhedron has edges of three different lengths and faces ...

Tutte (1971/72) conjectured that there are no 3-connected nonhamiltonian bicubic graphs. However, a counterexample was found by J. D. Horton in 1976 (Gropp 1990), and several ...

A circuit in which an entire graph is traversed in one route. Examples of curves that can be traced unicursally are the Mohammed sign and unicursal hexagram. The numbers of ...

The upper domination number Gamma(G) of a graph G is the maximum size of a minimal dominating set of vertices in G. The (lower) domination number may be similarly defined as ...