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The Matrix-Tree Theorem

  • Richard P. Stanley
Chapter
  • 5.4k Downloads
Part of the Undergraduate Texts in Mathematics book series (UTM)

Abstract

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.

Keywords

Matrix Tree Theorem Multiple Edges Binet-Cauchy Theorem Reduced Incidence Matrix Bottom Left Block 
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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  • Richard P. Stanley
    • 1
  1. 1.Department of MathematicsMassachusetts Institute of TechnologyCambridgeUSA

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