On abelian \(\ell \)-towers of multigraphs

We study how the \(\ell \)-adic valuation of the number of spanning trees varies in regular abelian \(\ell \)-towers of multigraphs. We show that for an infinite family of regular abelian \(\ell \)-towers of bouquets, the \(\ell \)-adic valuation of the number of spanning trees behaves similarly to the \(\ell \)-adic valuation of the class numbers in \({\mathbb {Z}}_{\ell }\)-extensions of number fields.