DOAJ Open Access 2025

THE TRIPLE IDEMPOTENT GRAPH OF THE RING Z_n

Vika Yugi Kurniawan Bayu Purboutomo Nughthoh Arfawi Kurdhi

Abstrak

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 .

Topik & Kata Kunci

Probabilities. Mathematical statistics

Penulis (3)

Vika Yugi Kurniawan

Bayu Purboutomo

Nughthoh Arfawi Kurdhi

Format Sitasi

APA MLA BibTeX

Kurniawan, V.Y., Purboutomo, B., Kurdhi, N.A. (2025). THE TRIPLE IDEMPOTENT GRAPH OF THE RING Z_n. https://doi.org/10.30598/barekengvol19iss3pp2219-2228

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Informasi Jurnal

Tahun Terbit: 2025
Sumber Database: DOAJ
DOI: 10.30598/barekengvol19iss3pp2219-2228
Akses: Open Access ✓