  Let $I(G)$ be a topological index of a graph. If $I(G+e)<I(G)$ (or
$I(G+e)>I(G)$, respectively) for each edge $e\not\in G$, then $I(G)$ is
monotonically decreasing (or increasing, respectively) with the addition of
edges. In this article, we present lower or upper bounds for some monotonic
topological indices, including the Wiener index, the hyper-Wiener index, the
Harary index, the connective eccentricity index, the eccentricity distance sum
of bipartite graphs in terms of the number of cut edges, and characterize the
corresponding extremal graphs, respectively.
