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 Sz(e)*P (H) = Sigma(e=uvEH) (m(u)(e|H) + m(0)(e|H)/2)(m(v)(e|H) + 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 m0(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.