The m-Clean Graph of a Finite Commutative Ring

Authors

Susan F. El-Deken, Department of Mathematics, Faculty of Science, Capital University, Ain Helwan, 11790, Helwan, EgyptFollow
Harald Fripertinger, Institute of Mathematics and Scientific Computing, NAWI-Graz, University of Graz, Heinrichstr. 36/4, A–8010, Graz, AustriaFollow
Aya Gamal, Department of Mathematics, Faculty of Science, Capital University, Ain Helwan, 11790, Helwan, EgyptFollow

ORCID

Susan F. El-Deken: https://orcid.org/0000-0001-5982-8011

Harald Fripertinger: https://orcid.org/0000-0001-7449-8532

Aya Gamal: https://orcid.org/0009-0006-3598-5673

Keywords

finite commutative rings, m-potent rings, clean rings, clean graphs, m-clean graphs

Article Type

Original Article

Abstract

We study m-clean graphs of finite commutative rings R, which are a generalization of clean graphs. Their vertices are pairs of m-potent elements and units of R. These graphs can be described as Cartesian sums or co-normal products of two graphs. In particular we explore under which conditions the subgraph involving only non-zero m-potent elements is connected and we determine the degrees of its vertices. Moreover, we characterize under which conditions on two rings the corresponding m-clean graphs are isomorphic.

How to Cite

El-Deken, Susan F.; Fripertinger, Harald; and Gamal, Aya (2025) "The m-Clean Graph of a Finite Commutative Ring," Sustainable Machine Intelligence Journal: Vol. 13: Iss. 1, Article 6.
DOI: https://doi.org/10.63689/3005-3617.1077

Creative Commons License

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