Release Time:2019-03-09  Hits:

Indexed by: Journal Article

Date of Publication: 2014-08-01

Journal: JOURNAL OF ALGEBRA AND ITS APPLICATIONS

Included Journals: Scopus、SCIE

Volume: 13

Issue: 5

ISSN: 0219-4988

Key Words: Iteration digraph; cycle; symmetric digraph; semiregular digraph

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 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.