THE DIGRAPH OF THE SQUARE MAPPING ON QUOTIENT RINGS OVER THE GAUSSIAN INTEGERS-Reference-Cited by-同舟云学术

THE DIGRAPH OF THE SQUARE MAPPING ON QUOTIENT RINGS OVER THE GAUSSIAN INTEGERS

Published:2011-05 Issue:03 Volume:07 Page:835-852
ISSN:1793-0421
Container-title:International Journal of Number Theory
language:en
Short-container-title:Int. J. Number Theory

Author:

MEEMARK YOTSANAN¹²,MAINGAM NAWAPHON¹²

Affiliation:

1. Department of Mathematics, Faculty of Science, Chulalongkorn University, Bangkok 10330, Thailand

2. Center of Excellence in Mathematics, CHE, Si Ayuthaya Road, Bangkok 10400, Thailand

Abstract

In this work, we investigate the structure of the digraph [Formula: see text] associated with the square mapping on the ring of Gaussian integers by using the exponent of the unit group modulo γ. The formula for the fixed points of [Formula: see text] is established. Some connections of the lengths of cycles with the exponent of the unit group modulo γ are presented. Furthermore, we study the maximum distance from the cycle on each component.

Publisher

World Scientific Pub Co Pte Lt

Subject

Algebra and Number Theory

Link

https://www.worldscientific.com/doi/pdf/10.1142/S1793042111004459

Reference5 articles.

1. Note on a new number theory function

2. The Euler φ-Function in the Gaussian Integers

3. Finding Factors of Factor Rings over the Gaussian Integers

4. On a Connection of Number Theory with Graph Theory

5. Structure of digraphs associated with quadratic congruences with composite moduli

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1. On the uniqueness of the factorization of power digraphs modulo $n$;Rendiconti del Seminario Matematico della Università di Padova;2018-11-19

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