On the Wiener Polarity Index∗
نویسندگان
چکیده
The Wiener polarity indexWP (G) of a graph G is the number of unordered pairs of vertices {u, v} of G such that the distance of u and v is equal to 3. In this paper, we obtain the relation between Wiener polarity index and Zegreb indices, and the relation between Wiener polarity index and Wiener index (resp. hyper-Wiener index). Moreover, we determine the second smallest Wiener polarity index together with the corresponding graphs among all trees on n vertices, we also identify the smallest and the second smallest Wiener polarity indices together with the corresponding graphs, respectively, among all unicyclic graphs on n vertices.
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