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In order to establish the mathematical basis for connections between molecular structures and physicochemical properties of chemical compounds, some topological indices have been put forward. Among them, the Wiener index is one of the most important topological indices. The sum of distances of all pairs of vertices in a connected graph is known as Wiener index or Wiener number. All structural formulas of chemical compounds are molecular graphs where vertices represent the set of atoms and edges represent chemical bonds. A graph is said to be detour saturated if the addition of any edge results in an increased greatest path length. The characteristic graph of a given benzenoid graph consists of vertices corresponding to hexagonal rings of the graph; two vertices are adjacent if and only if the corresponding rings share an edge. A benzenoid graph is called Cata-condensed if its characteristic graph is a tree. In this paper, we derive Wiener indices for characteristic graphs of benzenoid graphs in the form of hexagonal rings, which are detour-saturated trees.