The Kirchhoff's Matrix-Tree Theorem revisited: counting spanning trees with the quantum relative entropy
Quantum Physics
2011-02-14 v1 Information Theory
Combinatorics
math.IT
Abstract
By revisiting the Kirchhoff's Matrix-Tree Theorem, we give an exact formula for the number of spanning trees of a graph in terms of the quantum relative entropy between the maximally mixed state and another state specifically obtained from the graph. We use properties of the quantum relative entropy to prove tight bounds for the number of spanning trees in terms of basic parameters like degrees and number of vertices.
Cite
@article{arxiv.1102.2398,
title = {The Kirchhoff's Matrix-Tree Theorem revisited: counting spanning trees with the quantum relative entropy},
author = {Vittorio Giovannetti and Simone Severini},
journal= {arXiv preprint arXiv:1102.2398},
year = {2011}
}
Comments
12 pages