The Cubic Mapping Digraphs of Finite Commutative Rings

Main Article Content

Ittiwat Tocharoenirattisai

Abstract

Let R be a finite commutative ring with identity. We study the cubic mapping digraphs G(R) whose vertex set is R and there is a directed edge from a to b if and only if a^3 = b. We investigate the structure of digraph and establish theorems about fixed points, t−cycles and semiregularity. In addition, we work on the structure of digraphs for 2 and 3 components.

Downloads

Download data is not yet available.

Article Details

How to Cite
Tocharoenirattisai, I. (2020). The Cubic Mapping Digraphs of Finite Commutative Rings. วารสารคณิตศาสตร์, 65(700), 41 - 52. Retrieved from https://ph02.tci-thaijo.org/index.php/MJMATh/article/view/214818
Section
Research Article

References

[1] Bini, G., and Flamini, F. (2002). Finite Commutative Rings and Their Applications. New York: Kluwer Accademic Publishers.

[2] Su, HD. Tang, GH., and Wei, YJ. (2012). The Square Mapping Graphs of Finite Commutative rings. Algebra Colloquium, 19, p. 569 - 580.

[3] Tang, GH., and Wei, YJ. (2015). The Iteration Digraphs of Finite Commutative Rings. Turkish Journal of Mathematics, 39, p. 872 - 883.

[4] Tocharoenirattisai, I., & Meemark, Y. (2017). Exponent of Local Ring Extensions of Galois Rings and Digraphs of the k^th Power Mapping. Turkish Journal of Mathematics, 41, p. 223 - 234.