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A (general) octahedron is a polyhedron having eight faces. Examples include the 4-trapezohedron, augmented triangular prism (Johnson solid J_(49)), bislit cube, Dürer solid, ...

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 symbol of the form {p,q,r,...} used to describe regular polygons, polyhedra, and their higher-dimensional counterparts. The symbol {p} denotes a regular polygon for integer ...

A tetrahedral ring is a term given in this work to a set of n regular tetrahedra joined face-to-face sharing a common edge (with internal conjoined faces removed). These ...

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 tube of radius r of a set gamma is the set of points at a distance r from gamma. In particular, if gamma(t) is a regular space curve whose curvature does not vanish, then ...

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 connected domination number of a connected graph G, denoted d(G), is the size of a minimum connected dominating set of a graph G. The maximum leaf number l(G) and ...

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 ...

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 ...