Computing weighted Szeged and PI indices from quotient graphs |
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Authors: | Niko Tratnik |
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Institution: | Faculty of Natural Sciences and Mathematics, University of Maribor, Maribor, Slovenia |
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Abstract: | The weighted (edge-)Szeged index and the weighted (vertex-)PI index are modifications of the (edge-)Szeged index and the (vertex-)PI index, respectively, because they take into account also the vertex degrees. As the main result of this article, we prove that if G is a connected graph, then all these indices can be computed in terms of the corresponding indices of weighted quotient graphs with respect to a partition of the edge set that is coarser than the Θ*-partition. If G is a benzenoid system or a phenylene, then it is possible to choose a partition of the edge set in such a way that the quotient graphs are trees. As a consequence, it is shown that for a benzenoid system, the mentioned indices can be computed in sublinear time with respect to the number of vertices. Moreover, closed formulas for linear phenylenes are also deduced. |
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Keywords: | benzenoid system phenylene quotient graph weighted PI index weighted Szeged index |
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