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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

23 authors · 45 co-authorship links

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  • Universitas Sulawesi Tenggara
  • The University of Sydney
  • Affiliation unknown
  • Different organisations
  • Same organisation
  • Affiliation unknown
  • Thicker line = more joint articles · bigger circle = more articles
Show as table
Co-authorOrganisationJoint articles
Siswanto SiswantoAffiliation unknown2
Chessa Fanny EkasiwiAffiliation unknown2
Putri WulandariUniversitas Sulawesi Tenggara2
Dewi Retno Sari SaputroAffiliation unknown1
Andjani Ayu Cahaya TanjungAffiliation unknown1
Ririn SetiyowatiAffiliation unknown1
Zahra Febrilia RachmawatiAffiliation unknown1
Sutrima SutrimaAffiliation unknown1
Purnami WidyaningsihAffiliation unknown1
Anas IvanniAffiliation unknown1
Zakia Nur Ramadhani PutriAffiliation unknown1
Ika Nur FitrianiThe University of Sydney1
Ade Safira SeptianyAffiliation unknown1
Sutanto SutantoAffiliation unknown1
Nabiella Zahra RizkitaAffiliation unknown1
Santoso Budi WiyonoAffiliation unknown1
Yogi Pasca PratamaAffiliation unknown1
Muhammad Bagus SistriatmajaAffiliation unknown1
Beny Trias OktoraAffiliation unknown1
Salju Indara Zeith GeisthAffiliation unknown1

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 5 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>