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THE TRIPLE IDEMPOTENT GRAPH OF THE RING Z_n

BAREKENG: Jurnal Ilmu Matematika dan Terapan · Vol. 19 No. 3 (2025) · pp. 2219–2228

DOI
10.30598/barekengvol19iss3pp2219-2228
ISSN
2615-3017, 1978-7227
Published
2025-07-01
Publisher
PATTIMURA UNIVERSITY
Language
eng
License
creativecommons.org/licenses/by-sa/4.0

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.

Collaboration network of the authors

24 authors · 41 co-authorship links · 4 across different organisations

Hover or tap a name to highlight its co-authors. Double-click to open the author's page.

  • Sebelas Maret University
  • National Dong Hwa University
  • Different organisations
  • Same organisation
  • Affiliation unknown
  • Thicker line = more joint articles · bigger circle = more articles
Show as table
Co-authorOrganisationJoint articles
Chessa Fanny EkasiwiSebelas Maret University2
Putri WulandariSebelas Maret University2
Dewi Retno Sari SaputroSebelas Maret University1
Andjani Ayu Cahaya TanjungSebelas Maret University1
Ririn SetiyowatiSebelas Maret University1
Zahra Febrilia RachmawatiSebelas Maret University1
Sutrima SutrimaSebelas Maret University1
Purnami WidyaningsihSebelas Maret University1
Anas IvanniSebelas Maret University1
Siswanto SiswantoSebelas Maret University1
Zakia Nur Ramadhani PutriSebelas Maret University1
Ika Nur FitrianiSebelas Maret University1
Ade Safira SeptianySebelas Maret University1
Siswanto SiswantoSebelas Maret University1
Nabiella Zahra RizkitaSebelas Maret University1
Sutanto SutantoSebelas Maret University1
Santoso Budi WiyonoSebelas Maret University1
Yogi Pasca PratamaSebelas Maret University1
Muhammad Bagus SistriatmajaSebelas Maret University1
Beny Trias OktoraNational Dong Hwa University1
Salju Indara Zeith GeisthSebelas Maret University1

Affiliations come from OpenAlex; journal OAI-PMH metadata carries none. Authors without an OpenAlex ID are matched by name, which can merge or split people.

Metadata source: OAI-PMH (metadata jurnal) https://ojs3.unpatti.ac.id/index.php/barekeng/oai, first harvested 5 Nov 2026, last seen 8 Nov 2026.
Original metadata (oai_dc) 
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	<dc:title xml:lang="en-US">THE TRIPLE IDEMPOTENT GRAPH OF THE RING Z_n</dc:title>
	<dc:creator>Kurniawan, Vika Yugi</dc:creator>
	<dc:creator>Purboutomo, Bayu</dc:creator>
	<dc:creator>Kurdhi, Nughthoh Arfawi</dc:creator>
	<dc:description xml:lang="en-US">Let &amp;nbsp;be a commutative ring, and &amp;nbsp;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 &amp;nbsp;are adjacent if and only if there exists &amp;nbsp;where &amp;nbsp;and &amp;nbsp;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 &amp;nbsp;and , provided that the graph is connected. Furthermore, &amp;nbsp;is Hamiltonian if n is a prime and , and Eulerian if n is a prime and .</dc:description>
	<dc:publisher xml:lang="en-US">PATTIMURA UNIVERSITY</dc:publisher>
	<dc:date>2025-07-01</dc:date>
	<dc:type>info:eu-repo/semantics/article</dc:type>
	<dc:type>info:eu-repo/semantics/publishedVersion</dc:type>
	<dc:format>application/pdf</dc:format>
	<dc:identifier>https://ojs3.unpatti.ac.id/index.php/barekeng/article/view/15930</dc:identifier>
	<dc:identifier>10.30598/barekengvol19iss3pp2219-2228</dc:identifier>
	<dc:source xml:lang="en-US">BAREKENG: Jurnal Ilmu Matematika dan Terapan; Vol 19 No 3 (2025): BAREKENG: Journal of Mathematics and Its Application; 2219-2228</dc:source>
	<dc:source>2615-3017</dc:source>
	<dc:source>1978-7227</dc:source>
	<dc:source>10.30598/barekengvol19iss3year2025</dc:source>
	<dc:language>eng</dc:language>
	<dc:relation>https://ojs3.unpatti.ac.id/index.php/barekeng/article/view/15930/10796</dc:relation>
	<dc:rights xml:lang="en-US">Copyright (c) 2025 Vika Yugi Kurniawan, Bayu Purboutomo, Nughthoh Arfawi Kurdhi</dc:rights>
	<dc:rights xml:lang="en-US">http://creativecommons.org/licenses/by-sa/4.0</dc:rights>
</oai_dc:dc>