The extremal unicyclic graphs with given diameter and minimum edge revised Szeged index

Let $H$ be a connected graph. The edge revised Szeged index of $H$ is defined as $S{z}_e^{\ast }(H)=\sum _{e=uv\in E_H}(m_u(e|H)+\frac{m_0(e|H)}{2})(m_v(e|H)+\frac{m_0(e|H)}{2})$, where $m_u(e|H)$ (resp., $m_v(e|H)$) is the number of edges whose distance to vertex $u$ (resp., $v$) is smaller than to vertex $v$ (resp., $u$), and $m_0(e|H)$ is the number of edges equidistant from $u$ and $v$. In this paper, the extremal unicyclic graphs with given diameter and minimum edge revised Szeged index are characterized.