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arXiv · 2404.01442

On the Sombor index of trees with degree restrictions

Eric O. D. Andriantiana·Valisoa R. M. Rakotonarivo
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Abstract

We study the Sombor index of trees with various degree restrictions. In addition to rediscovering that among all trees with a given degree sequence, the greedy tree minimises the Sombor index and the alternating greedy tree maximises it, we also provide a full characterisation of all trees that have those maximum or minimum values. Moreover, we compare trees with different degree sequences and deduce a few corollaries.

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Eric O. D. Andriantiana, Valisoa R. M. Rakotonarivo. 2024-04-01. On the Sombor index of trees with degree restrictions. https://arxiv.org/abs/2404.01442

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