THE ITERATION DIGRAPHS OF GROUP RINGS OVER FINITE FIELDS
2014 ◽
Vol 13
(05)
◽
pp. 1350162
◽
Keyword(s):
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.
2015 ◽
Vol 07
(01)
◽
pp. 1450064
◽
2008 ◽
Vol 04
(05)
◽
pp. 851-857
◽
2013 ◽
Vol Vol. 15 no. 2
(Combinatorics)
◽
2017 ◽
Vol 17
(03n04)
◽
pp. 1741006
1994 ◽
Vol 50
(2)
◽
pp. 327-335
2019 ◽
Vol 19
(05)
◽
pp. 2050084