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The edge-Wiener index $W_e(G)$ of a connected graph $G$ is the sum ofdistances between all pairs of edges of $G$. A connected graph $G$ is said tobe 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 indexof graphs in $\mathcal{G}_{n,t}$ are identified and the corresponding extremalgraphs are characterized.

Bounds on the edge-Wiener index of cacti with $n$ vertices and $t$ cycles