Abstract
The Wiener index of a connected graph is the sum of distances between all pairs of distinct vertices, which is the oldest topological index related to molecular branching. In this paper we give a formula applied to compute the Wiener index of Θ-graphs. With the formula we determine the graphs having the minimum or maximum Wiener index among all Θ-graphs with a fixed order and characterize the graphs having the minimum Wiener index among all bicyclic graphs with perfect matchings.
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