The Wiener index W(G) of a connected graph G is defined as the half of the sum of the distances between every pair of vertices of G. It gives a good correlation with the thermodynamic properties of saturated hydrocarbon molecules. It is also know that the Wiener index of a molecular graph correlates with certain physical and chemical properties of a molecule. In this paper Wiener index of one-vertex union of fans Fn and flags Fln are determined.
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