The edge Szeged index of a graph $G$ is defined as $Sz_{ e}(G)=\sum\limits_{ uv\in E(G)}m_{ u}(uv|G)m_{ v}(uv|G)$, where $m_{ u}(uv|G)$ (resp., $m_{ v}(uv|G)$) is the number of edges whose distance to vertex $u$ (resp., $v$) is smaller than the distance to vertex $v$ (resp., $u$), respectively. In this paper, we characterize the graph with minimum edge Szeged index among all the unicyclic graphs with given order and diameter.
Categories: math.CO