Table 1 Graph-theoretic notation
Symbol | Designation |
|---|---|
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 |
Branch-height 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 k-branch-leaf number of T |
\(\text {bh}_k(T)\) | The k-branch height of T |