Some Results Concerning Directed Graphs Over Commutative Rings

Authors

DOI:

https://doi.org/10.31185/wjps.499

Abstract

This paper delves into the idea of a directed graph that presented and illustrated, A directed graph for every finite, commutative ring is presented in this paper by utilizing the additive and multiplicative properties. This is achieved based on the mapping (a, b) → (a + b, a • b). The essential objective of this research work is to examine the characteristics of these directed graphs, specifically the valuable information they offer about the ring itself. To this end, we have adopted and presented several theorems and Corollaries with their proofs to support the obtained results

 

References

R. Frucht, “Graphs of degree three with a given abstract group,” Can. J. Math. , 1, pp. 365–378, 1949.

David F. Anderson, T. Asir, Ayman Badawi and T. Tamizh Cheluva, “Graphs from rings,” Springer International Publishing, 2021.

Istvan Beck, “Coloring of commutative rings, Journal of Algebra,” vol. 116, no. 1, pp. 208–226, 1988.

V. Ramanathan , “On projective intersection graph of ideals of commutative rings,” Journal of Algebra and Its Applications,Vol. 20, No. 02, 2150017, 2021.

H. Muhammad, N. Qonita, R. A. W. Fibriyanti and Y. Susanti, “Bipartite graph associated with elements and cosets of subrings of finite rings, Barekeng,” Journal of Mathematics and Its Applications, vol. 17, iss. 2, pp.

-0672, June, 2023.

Mehsin Jabel Atteya, “New types of permuting n-Derivations with Their Applications on Associative Rings,” Symmetry, 12 (1), 46, 2020, https://doi.org/10.3390/sym12010046.

Atiyah, M. Macdonald, I., “Introduction to Commutative Algebra,” Addison-Wesley, Great Britain, 1969.

Bollob´as, B., “Modern Graph Theory,” Springer, New York, 1998.

Gallian, J.A., “Contemporary abstract algebra, Brooks/Cole Cengage Learning,” Page 188 RHIT Undergrad. Math. J., Vol. 14, no. 2, 2010.

Hungerford, T. W., Algebra, Springer-Verlag, 1989.

Kaplansky, I.., “Commutative Rings,” Polygonal Publishing House, 1974.

P. M. Cohen, “Further algebra and application s,” Springer – Verlag London Berlin Heidelberg , 1st Edition ,ISBN 978-1-4471-1120-7,2003.

Seth Hausken and Jared Skinner, “directed graphs of commutative rings,” Rose-Hulman Undergraduate Mathematics Journal, Vol.14: Iss 2, Article 11. https//scholar. Rose- ulman .edu/rhumj/vol14/iss2/11.

Downloads

Published

2024-09-30

Issue

Vol. 3 No. 3 (2024)

Section

Mathematics

License

Copyright (c) 2024 Ansam Abdul Hadi Mahmood

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

How to Cite

Abdul Hadi Mahmood, A. (2024). Some Results Concerning Directed Graphs Over Commutative Rings. Wasit Journal for Pure Sciences , 3(3), 69-73. https://doi.org/10.31185/wjps.499