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The \emph{Wiener index} is a widely studied topological index of graphs. Oneof the main problems in the area is to determine which graphs of givenproperties attain the extremal values of Wiener index.  In this paper we resolve an open problem posed by Du in 2012. To this end wedetermine the unicyclic bipartite graphs with given size of parts having themaximum Wiener index. This completes the previous research in which the minimumcase was solved.

Maximum Wiener index of unicyclic graphs with given bipartition