  This paper explores Iwasawa theory from a graph theoretic perspective,
focusing on the algebraic and combinatorial properties of Cayley graphs. Using
representation theory, we analyze Iwasawa-theoretic invariants within
$\mathbb{Z}_\ell$-towers of Cayley graphs, revealing connections between graph
theory, number theory, and group theory. Key results include the factorization
of associated Iwasawa polynomials and the decomposition of $\mu$- and
$\lambda$-invariants. Additionally, we apply these insights to complete graphs,
establishing conditions under which these invariants vanish.
