Abstract The edge-Szeged index of a graph G is defined as S z e ( G ) = ∑ u v ∈ E ( G ) m u ( u v | G ) m v ( u v | G ) , where m u ( u v | G ) (resp., m v ( u v | 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 graphs with minimum edge-Szeged index among all the unicyclic graphs with given order and perfect matchings.

中文翻译：

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具有完美匹配的单环图的边-Szeged索引

摘要 图 G 的边 Szeged 索引定义为 S ze ( G ) = ∑ uv ∈ E ( G ) mu ( uv | G ) mv ( uv | G ) ，其中 mu ( uv | G ) (resp., mv ( uv | G ) ) 分别是到顶点 u (resp., v ) 的距离小于到顶点 v (resp., u ) 的距离的边数。在本文中，我们在所有具有给定顺序和完美匹配的单环图中刻画了具有最小边 Szeged 指数的图。