Iwasawa theory of (directe) Cayley graphs

Abstract: In this article, we prove the Defect Conjecture for Cayley graphs of abelian groups, dihedral groups, and groups of the form $$\mathbb{Z}/p\mathbb{Z} \rtimes \mathbb{Z}/(p-1)\mathbb{Z}$$ where $p\geq 3$ is a prime. We also compute the Iwasawa invariants of the Bowen--Franks groups associated with these graphs in several cases.