Abstract
The Wiener index of a graphG is equal to the sum of distances between all pairs of vertices ofG. It is known that the Wiener index of a molecular graph correlates with certain physical and chemical properties of a molecule. In the mathematical literature, many good algorithms can be found to compute the distances in a graph, and these can easily be adapted for the calculation of the Wiener index. An algorithm that calculates the Wiener index of a tree in linear time is given. It improves an algorithm of Canfield, Robinson and Rouvray. The question remains: is there an algorithm for general graphs that would calculate the Wiener index without calculating the distance matrix? Another algorithm that calculates this index for an arbitrary graph is given.
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Work supported in part by the Research Council of Slovenia, Yugoslavia.
This work was done while both authors were visiting the Simon Fraser University.
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Mohar, B., Pisanski, T. How to compute the Wiener index of a graph. J Math Chem 2, 267–277 (1988). https://doi.org/10.1007/BF01167206
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DOI: https://doi.org/10.1007/BF01167206