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论文类型：期刊论文

发表时间：2014-08-01

发表刊物：JOURNAL OF ALGEBRA AND ITS APPLICATIONS

收录刊物：SCIE、Scopus

卷号：13

期号：5

ISSN号：0219-4988

关键字：Iteration digraph; cycle; symmetric digraph; semiregular digraph

摘要：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 alpha is an element of R to b is an element of R if b = alpha(k). In this paper, we investigate the iteration digraphs G(F(p)rC(n), k) of F(p)rC(n), the group ring of a cyclic group C-n over a finite field F(p)r. We study the cycle structure of G(F(p)rC(n), k), and explore the symmetric digraphs. Finally, we obtain necessary and sufficient conditions on F(p)rC(n) and k such that G(F(p)rC(n), k) is semiregular.