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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. ...

There are several equivalent definitions of a closed set. Let S be a subset of a metric space. A set S is closed if 1. The complement of S is an open set, 2. S is its own set ...

Let K subset V subset S^3 be a knot that is geometrically essential in a standard embedding of the solid torus V in the three-sphere S^3. Let K_1 subset S^3 be another knot ...

A coordinate chart is a way of expressing the points of a small neighborhood, usually on a manifold M, as coordinates in Euclidean space. An example from geography is the ...