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Algorithm. Appl."],"published-print":{"date-parts":[[2020,8]]},"abstract":"<jats:p> The Wiener index of a connected graph is the sum of the distance of all pairs of distinct vertices. It was introduced by Wiener in 1947 to analyze some aspects of branching by fitting experimental data for several properties of alkane compounds. Denote by [Formula: see text] the set of unicyclic graphs with [Formula: see text] vertices and [Formula: see text] vertices of even degree. 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