On the differences between Szeged and Wiener indices of graphs (Q641199)

Let \(n(G)\) be the difference of the Wiener and Szeged indices of a connected graph \(G\). In the present paper, a path-edge matrix for the graph \(G\) is presented by which it is possible to classify the graphs in which \(n(G) = 2\). It is shown that there is no graph \(G\) with the property that \(n(G) = 1\) or 3. It is also shown that, for a given positive integer \(k\) other than 1 and 3, there exists a graph \(G\) with \(n(G) = k\).