BAREKENG: Jurnal Ilmu Matematika dan Terapan
Vol 19 No 3 (2025): BAREKENG: Journal of Mathematics and Its Application

THE TRIPLE IDEMPOTENT GRAPH OF THE RING Z_n

Kurniawan, Vika Yugi (Unknown)
Purboutomo, Bayu (Unknown)
Kurdhi, Nughthoh Arfawi (Unknown)

Article Info

Publish Date
01 Jul 2025

Abstract

Let be a commutative ring, and denote the set of all idempotent elements of . The triple idempotent graph of , denoted by , is defined as an undirected simple graph whose vertex set . Two distinct vertices u and v in are adjacent if and only if there exists where and such that , and . This definition generalizes the notion of an idempotent divisor graph by involving a triple product, which allows deeper exploration of the combinatorial behavior of idempotents in rings. In this research, we investigate the properties of the triple idempotent graph of the ring of integers modulo n, denoted by . As a results, we establish that and , provided that the graph is connected. Furthermore, is Hamiltonian if n is a prime and , and Eulerian if n is a prime and .

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Journal Info
BAREKENG: Jurnal Ilmu Matematika dan Terapan
Website

Abbrev

barekeng

Publisher

Universitas Pattimura

Subject

Computer Science & IT Control & Systems Engineering Economics, Econometrics & Finance Energy Engineering Mathematics Mechanical Engineering Physics Transportation

Description

BAREKENG: Jurnal ilmu Matematika dan Terapan is one of the scientific publication media, which publish the article related to the result of research or study in the field of Pure Mathematics and Applied Mathematics. Focus and scope of BAREKENG: Jurnal ilmu Matematika dan Terapan, as follows: - Pure ...