On the Natural Imprint Function of a Graph

A subgraph H of a graph G is gated if for every x V(G) there exists a vertex u in H such that dG (x, v) = dG (x, u) + d G (u, v) for any v V(H). The gated amalgam of graphs G 1 and G2 is obtained from G1 and G2 by identifying their isomorphic gated subgraphs H1 and H2 . Two theorems on the Wiener index of gated amalgams are proved. Several known results on the Wiener index of (chemical) graphs are corollaries of these theorems which we demonstrate by gated amalgams of trees and benzenoid systems. Document Type: Article View references (32) Select: Allgfedc

• Type: Journal
• Year: 2002
• Where: EJC
• Authors: Bostjan Bresar
• Keywords: EJC 2002, Gated Amalgams, Information Technology, Theorems, Wiener Index