Tripotent Divisor Graph of a Commutative Ring

Luma A. Khaleel, Husam Q. Mohammad, Nazar H. Shuker and Abdul Rauf Khan

International Journal of Mathematics and Mathematical Sciences, 2024, vol. 2024, 1-9

Abstract: In this work, we introduce a new concept called the tripotent divisor graph of a commutative ring. It is defined with vertices set in a ring R, where distinct vertices r1 and r2 are connected by an edge if their product belongs to the set of all nonunite tripotent in R. We denote this graph as 3I ΓR. We utilize this graph to examine the role of tripotent elements in the structure of rings. Additionally, we provide various findings regarding graph-theoretic characteristics of this graph, including its diameter, vertex degrees, and girth. Furthermore, we investigate the size, central vertices, and distances between vertices for the tripotent divisor graph formed by the direct product of two fields.

Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:1954058

DOI: 10.1155/2024/1954058

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