Tripotent Graph of Finite Rings

Haval M. Mohammed Salih

Abstract


In this paper, we find the number of non-trivial tripotent elements for some finite rings, namely ℤn, H(𝔽q), and 𝔽qCn. For this purpose, we find the general formula of them. Furthermore, we introduce the tri-potent graph of a finite ring R, denoted by Tri(R), where two distinct vertices x and y in R with a<b are adjacent if and only if a − b ∈ Tri(R). It is shown that the tri-potent graph is a bi-regular connected with girth at most 4. Also, the tri potent graph of ℤn is bipartite graph for some n.

Keywords


Tripotent Graph, Chinese Remainder Theorem, Girth, Connectedness

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DOI: http://dx.doi.org/10.19184/ijc.2026.10.1.1

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