Zeta functions of finite Schreier graphs and their zig-zag products-Reference-Cited by-同舟云学术

Zeta functions of finite Schreier graphs and their zig-zag products

Published:2016-08-09 Issue:08 Volume:16 Page:1750151
ISSN:0219-4988
Container-title:Journal of Algebra and Its Applications
language:en
Short-container-title:J. Algebra Appl.

Author:

Shaikh Asif¹²,Bhate Hemant²

Affiliation:

1. Department of Mathematics and Statistics, R. A. Podar College of Commerce and Economics, Mumbai 400019, India

2. Department of Mathematics, Savitribai Phule Pune University, Pune 411007, India

Abstract

We investigate the Ihara zeta functions of finite Schreier graphs [Formula: see text] of the Basilica group. We show that [Formula: see text] is two sheeted unramified normal covering of [Formula: see text], for all [Formula: see text] with Galois group [Formula: see text] In fact, for any [Formula: see text], the graph [Formula: see text] is [Formula: see text] sheeted unramified, non-normal covering of [Formula: see text]. In order to do this, we give the definition of the [Formula: see text] [Formula: see text] [Formula: see text] of Schreier graphs of Basilica groups. We also show the corresponding results in zig-zag product of Schreier graphs [Formula: see text] with a [Formula: see text]-cycle.

Publisher

World Scientific Pub Co Pte Lt

Subject

Applied Mathematics,Algebra and Number Theory

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0219498817501511

Reference11 articles.

1. On one-factorizations of replacement products

2. Schreier graphs of the Basilica group

3. Partition Functions of the Ising Model on Some Self-similar Schreier Graphs

4. Connectedness and Isomorphism Properties of the Zig-Zag Product of Graphs

5. Zeta Functions of Heisenberg Graphs over Finite Rings