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јвтор:  Goubko M.
Ќазвание:  Maximizing Wiener index for trees with given vertex weight and degree sequences
—татус:  опубликовано
√од:  2018
“ип публикации:  стать€ вед.журн.
Ќазвание журнала или конференции:  Applied Mathematics and Computation
Ќомер (том) журнала:  316
ѕолна€ библиографическа€ ссылка:  Goubko M. Maximizing Wiener index for trees with given vertex weight and degree sequences // Applied Mathematics and Computation, 2018, Vol. 316, P. 102Ц114.
јннотаци€:  The Wiener index is maximized over the set of trees with the given vertex weight and degree sequences. This model covers the traditional УunweighedФ Wiener index, the terminal Wiener index, and the vertex distance index. It is shown that there exists an optimal caterpillar. If weights of internal vertices increase in their degrees, then an optimal caterpillar exists with weights of internal vertices on its backbone monotonously increasing from some central point to the ends of the backbone, and the same is true for pendent vertices. A tight upper bound of the Wiener index value is proposed and an efficient greedy heuristics is developed that approximates well the optimal index value. Finally, a branch and bound algorithm is built and tested for the exact solution of this NP-complete problem.

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