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The m-Clean Graph of a Finite Commutative Ring |
Sustainable Machine Intelligence Journal 13(1), Article 6 (2021). DOI 10.63689/3005-3617.1077.
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.
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GDPR | The m-Clean Graph of a Finite Commutative Ring |  |