Iwasawa Theory of graphs and their duals

TL;DR

This paper explores the Iwasawa theory related to ramified $bZ_p^d$-extensions of finite connected graphs and their duals, extending algebraic number theory concepts to graph structures.

Contribution

It introduces the Iwasawa theory framework for graphs and their duals, a novel application of number theory principles to graph theory.

Findings

Developed Iwasawa modules for graph extensions

Analyzed ramification in $bZ_p^d$-extensions of graphs

Extended Iwasawa theory to dual graph structures

Abstract

In this article, we study questions pertaining to ramified $\mathbb{Z}_p^d$-extensions of a finite connected graph $X$. We also study the Iwasawa theory of dual graphs.