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Table 1 Graph-theoretic notation

From: A novel method for inference of acyclic chemical compounds with bounded branch-height based on artificial neural networks and integer programming

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