  The edge-Wiener index $W_e(G)$ of a connected graph $G$ is the sum of
distances between all pairs of edges of $G$. A connected graph $G$ is said to
be a cactus if each of its blocks is either a cycle or an edge. Let
$\mathcal{G}_{n,t}$ denote the class of all cacti with $n$ vertices and $t$
cycles. In this paper, the upper bound and lower bound on the edge-Wiener index
of graphs in $\mathcal{G}_{n,t}$ are identified and the corresponding extremal
graphs are characterized.

Combinatorics