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All Journal Indonesian Journal of Combinatorics
Haval M. Mohammed Salih
Soran University
Computer Science & IT Decision Sciences, Operations Research & Management

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Tripotent graph of finite rings Haval M. Mohammed Salih
Indonesian Journal of Combinatorics Vol 10, No 1 (2026)
Publisher : Indonesian Combinatorial Society (InaCombS)

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.19184/ijc.2026.10.1.1

Abstract

In this paper, we find the number of non-trivial tripotent elements for some finite rings, namely ℤn, H(?q), and ?q Cn. 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.
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