Abstract
In this paper, we will consider the Wiener index for a class of trees that is connected to partitions of integers. Our main theorem is the fact that every integer \(\geq 470\) is the Wiener index of a member of this class. As a consequence, this proves a conjecture of Lepović and Gutman. The paper also contains extremal and average results on the Wiener index of the studied class.
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This work was supported by Austrian Science Fund project no. S-8307-MAT.
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Wagner, S.G. A Class of Trees and its Wiener Index. Acta Appl Math 91, 119–132 (2006). https://doi.org/10.1007/s10440-006-9026-5
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DOI: https://doi.org/10.1007/s10440-006-9026-5