The Kirchhoff's Matrix-Tree Theorem revisited: counting spanning trees with the quantum relative entropy

Details The Kirchhoff's Matrix-Tree Theorem revisited: counting spanning trees with the quantum relative entropy The Kirchhoff's Matrix-Tree Theorem revisited: counting spanning trees with the quantum relative entropy

2011-02-11

arxiv.org/abs/1102.2398v1

Physics

Quantum Physics

12 pages

Scientific paper

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.

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