General graph notation

\(H = (V, E)\)

A graph H with a vertex set V and edge set E

V(H)

The vertex set of a graph H

E(H)

The edge set of a graph H

\(N_H(v)\)

The number of neighbors of a vertex v in a graph H

\(\deg _H(v)\)

The degree \(N_H(v)\) of a vertex v in a graph H

\({{\text {dist}}}_H(u, v)\)

The distance between two vertices u and v in a graph H

\(\text {dia}(H)\)

The diameter of a graph H

\(\ell (P)\)

The length of a path P

Branchheight in a tree T

\(V^{{\text {in}}}\)

The set of internal vertices for a fixed branch parameter k

\(V^{\text {ex}}\)

The set of external vertices for a fixed branch parameter k

\(E^{{\text {in}}}\)

The set of internal edges for a fixed branch parameter k

\(E^{\text {ex}}\)

The set of external edges for a fixed branch parameter k

\({\text {bl}}_k(T)\)

The kbranchleaf number of T

\(\text {bh}_k(T)\)

The kbranch height of T
