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A special graph vertex that is designated to turn a tree into a rooted tree or a graph into a rooted graph. The root is sometimes also called "eve," or an "endpoint" (Saaty ...

A tree is a mathematical structure that can be viewed as either a graph or as a data structure. The two views are equivalent, since a tree data structure contains not only a ...

Let G be a graph and S a subgraph of G. Let the number of odd components in G-S be denoted S^', and |S| the number of graph vertices of S. The condition |S|>=S^' for every ...

A Möbius ladder, sometimes called a Möbius wheel (Jakobson and Rivin 1999), of order n is a simple graph obtained by introducing a twist in a prism graph of order n that is ...

The arc set of a directed graph is the set of all arcs (directed edges) of the graph. The arc set for a directed graph g is given in the Wolfram Language by EdgeList[g].

The eigenvector corresponding to the second smallest eigenvalue (i.e., the algebraic connectivity) of the Laplacian matrix of a graph G. The Fiedler vector is used in ...

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 ...

The Tutte 8-cage (Godsil and Royle 2001, p. 59; right figure) is a cubic graph on 30 nodes and 45 edges which is the Levi graph of the Cremona-Richmond configuration. It ...

The girth of a graphs is the length of one of its (if any) shortest graph cycles. Acyclic graphs are considered to have infinite girth (Skiena 1990, p. 191). The girth of a ...

A straight line embedding, or "straight line drawing," of a graph is a graph embedding in which all edges are drawn as straight line segments (as opposed to curves, etc.).