q-Analog of Wiener Index

The Wiener index is the sum of distances between all pairs of vertices of a connected graph. In this paper we propose q-analogs of the Wiener index, motivated by the theory of hypergeometric series. The basic properties of these q-Wiener indices are established, as well as their relations with the Hosoya polynomial. Some possible chemical interpretations and applications of the q-Wiener indices are considered.

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