A formula for τ_G(M) is derived when M induces an acyclic subgraph and G-M has complete components, yielding counts for line graphs and a factorization property for graphs with clique cut-sets.
Mohar, The Laplacian Spectrum of Graphs, in Graph Theory, Combinatorics, and Applications 2, Y
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Formulas counting spanning trees in line graphs and their extensions
A formula for τ_G(M) is derived when M induces an acyclic subgraph and G-M has complete components, yielding counts for line graphs and a factorization property for graphs with clique cut-sets.