2021/06/21 by Sophia Gonet, Gonet, Sophia
Computer Science · Engineering · Mathematics · #Combinatorics (math.CO) #FOS: Mathematics #Graph theory and applications #Interconnection Networks and Systems #Number Theory (math.NT) #VLSI and FPGA Design Techniques
paper · pdf · doi:10.48550/arxiv.2106.11221
openalex publication_date 2021/06/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The Jacobian group (also known as the critical group or sandpile group) is an important invariant of a finite, connected graph X; it is a finite abelian group whose cardinality is equal to the number of spanning trees of X (Kirchhoff's Matrix Tree Theorem). A specific type of covering graph, called a derived graph, that is constructed from a voltage graph with voltage group G is the object of interest in this paper. Towers of derived graphs are studied by using aspects of classical Iwasawa Theory (from number theory). Formulas for the orders of the Sylow p-subgroups of Jacobians in an infinite voltage p-tower, for any prime p, are obtained in terms of classical μ and λ invariants by using the decomposition of a finitely generated module over the Iwasawa Algebra.