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Let $G$ be a connected graph. The revised edge Szeged index of $G$ is definedas $Sz^{\ast}_{e}(G)=\sum\limits_{e=uv\inE(G)}(m_{u}(e|G)+\frac{m_{0}(e|G)}{2})(m_{v}(e|G)+\frac{m_{0}(e|G)}{2})$, where$m_{u}(e|G)$ (resp., $m_{v}(e|G)$) is the number of edges whose distance tovertex $u$ (resp., $v$) is smaller than the distance to vertex $v$ (resp.,$u$), and $m_{0}(e|G)$ is the number of edges equidistant from both ends of$e$, respectively. In this paper, the graphs with minimum revised edge Szegedindex among all the unicyclic graphs with given diameter are characterized.

The extremal unicyclic graphs of the revised edge Szeged index with given diameter