Factorization of \(\mathbb C\)-valued functions induced by graphs. (English) Zbl 1353.05125
Summary: In this paper, we study certain \(\mathbb C\)-valued functions induced by given graphs called graph zeta functions. In particular, we are interested in factorizations of such functions. We show that the factorizations of graph zeta functions are characterized by certain subgraphs of given graphs. Based on this factorization property on graph zeta functions, we define-and-study the non-factorizability of graphs.
MSC:
| 05E15 | Combinatorial aspects of groups and algebras (MSC2010) |
| 05C20 | Directed graphs (digraphs), tournaments |
| 11G15 | Complex multiplication and moduli of abelian varieties |
| 11R04 | Algebraic numbers; rings of algebraic integers |
| 11R09 | Polynomials (irreducibility, etc.) |
| 11R47 | Other analytic theory |
| 11R56 | Adèle rings and groups |
| 46L10 | General theory of von Neumann algebras |
| 46L40 | Automorphisms of selfadjoint operator algebras |
| 46L53 | Noncommutative probability and statistics |
| 46L54 | Free probability and free operator algebras |
Keywords:
directed graphs; graph groupoids; Redei zeta functions; graph zeta-functions; factorizability on graphs; non-factorizable graphsReferences:
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