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The set closure St^_v of a star Stv at a vertex v of a simplicial complex K.

A set X is called a "cone" with vertex at the origin if for any x in X and any scalar a>=0, ax in X.

Given a positive integer n, a labeled n-digraph is a digraph whose vertex set is {1,...,n}.

A limb of a tree at a vertex v is the union of one or more branches at v in the tree. v is then called the base of the limb.

A simplicial complex K is said to be locally finite if each vertex of K belongs only to finitely many simplices of K.

The number of outward directed graph edges from a given graph vertex in a directed graph.

A ternary tree is a tree-like structure that is rooted and in which each vertex has at most three children.

Two nodes connected to the same node which are same distance from the root vertex in a rooted tree are called siblings. A function to return the siblings of a vertex v in a ...

A k-coloring of a graph G is a vertex coloring that is an assignment of one of k possible colors to each vertex of G (i.e., a vertex coloring) such that no two adjacent ...

Let G be a finite graph and v a vertex of G. The stabilizer of v, stab(v), is the set of group elements {g in Aut(G)|g(v)=v}, where Aut(g) is the graph automorphism group. ...