Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Linear algebraic techniques for spanning tree enumeration   Kirchhoff's Matrix-Tree Theorem asserts that the number of spanning trees in
a finite graph can be computed from the determinant of any of its reduced
Laplacian matrices. In many cases, even for well-studied families of graphs,
this can be computationally or algebraically taxing. We show how two well-known
results from linear algebra, the Matrix Determinant Lemma and the Schur
complement, can be used to elegantly count the spanning trees in several
significant families of graphs.

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The categories of this paper are: q-alg
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The categories of this paper are: solv-int
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The categories of this paper are: econ
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The categories of this paper are: eess
0
The categories of this paper are: hep-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: funct-an
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The categories of this paper are: mtrl-th
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The categories of this paper are: cond-mat
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The categories of this paper are: cmp-lg
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The categories of this paper are: comp-gas
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The categories of this paper are: q-bio
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The categories of this paper are: hep-th
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The categories of this paper are: alg-geom
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The categories of this paper are: q-fin