Abstract
The edge-Szeged index of a graph G is defined as Sze(G)=∑uv∈E(G)mu(uv|G)mv(uv|G), where mu(uv|G) (resp., mv(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 graphs with minimum edge-Szeged index among all the unicyclic graphs with given order and perfect matchings.
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