  In this paper, we prove a collection of results on graphical indices. We
determine the extremal graphs attaining the maximal generalized Wiener index
(e.g. the hyper-Wiener index) among all graphs with given matching number or
independence number. This generalizes some work of Dankelmann, as well as some
work of Chung. We also show alternative proofs for two recents results on
maximizing the Wiener index and external Wiener index by deriving it from
earlier results. We end with proving two conjectures. We prove that the maximum
for the difference of the Wiener index and the eccentricity is attained by the
path if the order $n$ is at least $9$ and that the maximum weighted Szeged
index of graphs of given order is attained by the balanced complete bipartite
graphs.
