On the further relation between the (revised) Szeged index and the Wiener index of graphs

In 2010, Hansen et al. proposed three conjectures on the differences between the (revised) Szeged index and the Wiener index for a connected graph GG. Recently, the above conjectures were solved by Chen et al. (2014). In this paper, as a continuance of it, we study some further relation between the (revised) Szeged index and Wiener index of connected graphs. Some sharp bounds on the difference between the (revised) Szeged index and Wiener index are established and the corresponding extremal graphs are characterized.