On Directed Graphs with the Same Sum over Arborescence Weights
Combinatorics
2026-03-13 v1
Abstract
We show that certain digraphs with the same vertex set but different arc sets have the same sum over the weights of all arborescences with a given root vertex. We relate our results to the Matrix-Tree Theorem and show how they provide a graphical approach for factoring matrix determinants.
Keywords
Cite
@article{arxiv.2603.11451,
title = {On Directed Graphs with the Same Sum over Arborescence Weights},
author = {Sayani Ghosh and Bradley S. Meyer},
journal= {arXiv preprint arXiv:2603.11451},
year = {2026}
}