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A point v is a central point of a graph if the eccentricity of the point equals the graph radius. The set of all central points is called the graph center.

Let a graph G have graph vertices with vertex degrees d_1<=...<=d_m. If for every i<n/2 we have either d_i>=i+1 or d_(n-i)>=n-i, then the graph is Hamiltonian.

A complete multipartite graph is a graph that is a complete k-partite graph for some positive integer k (Chartrand and Zhang 2008, p. 41).

A simple graph with n>=3 graph vertices in which each graph vertex has vertex degree >=n/2 has a Hamiltonian cycle.

An graph edge of a graph is separating if a path from a point A to a point B must pass over it. Separating graph edges can therefore be viewed as either bridges or dead ends.

The number of graph edges meeting at a given node in a graph is called the order of that graph vertex.

Every semisimple Lie algebra g is classified by its Dynkin diagram. A Dynkin diagram is a graph with a few different kinds of possible edges. The connected components of the ...

The hypercube is a generalization of a 3-cube to n dimensions, also called an n-cube or measure polytope. It is a regular polytope with mutually perpendicular sides, and is ...

Consider any star of n line segments through one point in space such that no three lines are coplanar. Then there exists a polyhedron, known as a zonohedron, whose faces ...

Given two intersecting lines or line segments, the amount of rotation about the point of intersection (the vertex) required to bring one into correspondence with the other is ...