The Matrix-Tree Theorem

Part of the Undergraduate Texts in Mathematics book series (UTM)


The Matrix-Tree Theorem is a formula for the number of spanning trees of a graph in terms of the determinant of a certain matrix. We begin with the necessary graph-theoretical background. Let G be a finite graph, allowing multiple edges but not loops. (Loops could be allowed, but they turn out to be completely irrelevant.


Matrix Tree Theorem Multiple Edges Binet-Cauchy Theorem Reduced Incidence Matrix Bottom Left Block 
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© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.Department of MathematicsMassachusetts Institute of TechnologyCambridgeUSA

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