On the Sombor index of trees with degree restrictions
Combinatorics
2024-04-03 v1
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.
Cite
@article{arxiv.2404.01442,
title = {On the Sombor index of trees with degree restrictions},
author = {Eric O. D. Andriantiana and Valisoa R. M. Rakotonarivo},
journal= {arXiv preprint arXiv:2404.01442},
year = {2024}
}
Comments
14 pages