On the differences between Szeged and Wiener indices of graphs |
| |
Authors: | MJ Nadjafi-Arani H Khodashenas AR Ashrafi |
| |
Institution: | aDepartment of Mathematics, Statistics and Computer Science, Faculty of Science, University of Kashan, Kashan 87317-51167, Islamic Republic of Iran |
| |
Abstract: | Let G be a connected graph and η(G)=Sz(G)−W(G), where W(G) and Sz(G) are the Wiener and Szeged indices of G, respectively. A well-known result of Klav?ar, Rajapakse, and Gutman states that η(G)≥0, and by a result of Dobrynin and Gutman η(G)=0 if and only if each block of G is complete. In this paper, a path-edge matrix for the graph G is presented by which it is possible to classify the graphs in which η(G)=2. It is also proved that there is no graph G with the property that η(G)=1 or η(G)=3. Finally, it is proved that, for a given positive integer k,k≠1,3, there exists a graph G with η(G)=k. |
| |
Keywords: | Szeged index Wiener index Block |
本文献已被 ScienceDirect 等数据库收录! |
|