On the extrema of the mean subtree order of graphs
Combinatorics
2025-08-29 v1
Abstract
It has been conjectured that the minimum and maximum of the mean subtree order among connected graphs of order are attained by the path and clique , respectively. Extending ideas due to Haslegrave and Vince, we confirm that the minimum is indeed attained by . On the other hand, we discuss different approaches (both promising and flawed) that could lead to a proof of the extremality of .
Cite
@article{arxiv.2508.20593,
title = {On the extrema of the mean subtree order of graphs},
author = {Stijn Cambie and Jorik Jooken and Stephan Wagner},
journal= {arXiv preprint arXiv:2508.20593},
year = {2025}
}
Comments
17 pages, 3 figures