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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 Z_-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 - and -invariants. Additionally, we apply these insights to complete graphs, establishing conditions under which these invariants vanish.
Ghosh et al. (Tue,) studied this question.
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