A Comprehensive Overview on the Formation of Homomorphic Copies in Coset Graphs for the Modular Group-Reference-Cited by-同舟云学术

A Comprehensive Overview on the Formation of Homomorphic Copies in Coset Graphs for the Modular Group

Published:2021-09-20 Issue: Volume:2021 Page:1-11
ISSN:2314-4785
Container-title:Journal of Mathematics
language:en
Short-container-title:Journal of Mathematics

Author:

Alolaiyan Hanan¹^ORCID,Razaq Abdul²^ORCID,Yousaf Awais³^ORCID,Zahra Rida⁴

Affiliation:

1. Department of Mathematics, King Saud University, Riyadh, Saudi Arabia

2. Department of Mathematics, Division of Science and Technology, University of Education Lahore, Lahore, Pakistan

3. Department of Mathematics, The Islamia University of Bahawalpur, Bahawalpur 63100, Pakistan

4. Department of Mathematics, Govt. Girls Elementary School Narri, Khushab, Pakistan

Abstract

This work deals with the well-known group-theoretic graphs called coset graphs for the modular group G and its applications. The group action of G on real quadratic fields forms infinite coset graphs. These graphs are made up of closed paths. When M acts on the finite field Zp, the coset graph appears through the contraction of the vertices of these infinite graphs. Thus, finite coset graphs are composed of homomorphic copies of closed paths in infinite coset graphs. In this work, we have presented a comprehensive overview of the formation of homomorphic copies.

Funder

King Saud University

Publisher

Hindawi Limited

Subject

General Mathematics

Link

http://downloads.hindawi.com/journals/jmath/2021/3905425.pdf

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