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- Title
THE ITERATION DIGRAPHS OF GROUP RINGS OVER FINITE FIELDS.
- Authors
WEI, YANGJIANG; TANG, GAOHUA; NAN, JIZHU
- 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(픽prCn, k) of 픽prCn, the group ring of a cyclic group Cn over a finite field 픽pr. We study the cycle structure of G(픽prCn, k), and explore the symmetric digraphs. Finally, we obtain necessary and sufficient conditions on 픽prCn and k such that G(픽prCn, k) is semiregular.
- Subjects
ITERATIVE methods (Mathematics); DIRECTED graphs; GRAPH theory; GROUP rings; FINITE fields; COMMUTATIVE rings; RINGS of integers
- Publication
Journal of Algebra & Its Applications, 2014, Vol 13, Issue 5, p-1
- ISSN
0219-4988
- Publication type
Article
- DOI
10.1142/S0219498813501624