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

YOTSANAN MEEMARK

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

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

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and

NAWAPHON MAINGAM

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

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

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https://doi.org/10.1142/S1793042111004459Cited by:1 (Source: Crossref)

Abstract

In this work, we investigate the structure of the digraph 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 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.

Keywords:

AMSC: 11R04, 05C20

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