Affiliation:
1. School of Mathematical Sciences, Guangxi Teachers Education University, Nanning, 530023, P. R. China
2. School of Mathematical Sciences, Dalian University of Technology, Dalian, 116024, P. R. China
Abstract
For a finite commutative ring R and a positive integer k ≥ 2, we construct an iteration digraph G(R, k) whose vertex set is R and for which there is a directed edge from a ∈ R to b ∈ R if b = ak. In this paper, we investigate the iteration digraphs G(𝔽prCn, k) of 𝔽prCn, the group ring of a cyclic group Cn over a finite field 𝔽pr. We study the cycle structure of G(𝔽prCn, k), and explore the symmetric digraphs. Finally, we obtain necessary and sufficient conditions on 𝔽prCn and k such that G(𝔽prCn, k) is semiregular.
Publisher
World Scientific Pub Co Pte Lt
Subject
Applied Mathematics,Algebra and Number Theory
Cited by
2 articles.
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1. Digraph from power mapping on noncommutative groups;Journal of Algebra and Its Applications;2019-05-03
2. On the uniqueness of the factorization of power digraphs modulo $n$;Rendiconti del Seminario Matematico della Università di Padova;2018-11-19