On abelian $\mathrm{\ell }$-towers of multigraphs

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