Linear Algebraic Techniques for Spanning Tree Enumeration

DOI10.1080/00029890.2020.1708171zbMath1437.05106arXiv1903.04973OpenAlexW3104523297MaRDI QIDQ4960434

Steven Klee, Matthew T. Stamps

Publication date: 16 April 2020

Published in: The American Mathematical Monthly (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1903.04973

zbMATH Keywords

Schur complementKirchhoff's matrix-tree theoremmatrix determinant lemma

Mathematics Subject Classification ID

Trees (05C05) Enumeration in graph theory (05C30) Graphs and linear algebra (matrices, eigenvalues, etc.) (05C50)

Related Items (5)

Spanning tree enumeration and nearly triangular graph Laplacians ⋮ Biconed graphs, weighted forests, and \(h\)-vectors of matroid complexes ⋮ Multidimensional Lambert-Euler inversion and vector-multiplicative coalescent processes ⋮ Effective resistances and spanning trees in the complete bipartite graph plus a matching ⋮ Spanning trees of descendants of a complete graph

Cites Work

• The number of spanning trees of a complete multipartite graph
• Degree maximal graphs are Laplacian integral
• Enumerative properties of Ferrers graphs
• Threshold graphs and related topics
• Laplacian spectra and spanning trees of threshold graphs
• Linear algebraic techniques for weighted spanning tree enumeration
• The Enumeration of Point Labelled Chromatic Graphs and Trees
• Proofs from THE BOOK
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