Melola Discovery

← Melola Discovery

Open access Jurnal SINTA 3

THE TRIPLE IDENTITY GRAPH OF THE RING Z_n

BAREKENG: Jurnal Ilmu Matematika dan Terapan · Vol. 19 No. 4 (2025) · pp. 2521–2530

DOI
10.30598/barekengvol19iss4pp2521-2530
ISSN
2615-3017, 1978-7227
Published
2025-09-01
Publisher
PATTIMURA UNIVERSITY
Language
eng
License
creativecommons.org/licenses/by-sa/4.0

Abstract

Let be a commutative ring with identity and is an identity element of. The triple identity graph of the ring, represented by ), is an undirected simple graph with the vertex set. In, two different vertices and is called adjacent if there is an element such that and. The triple identity graph of the ring of integers modulo, represented by, is the subject of this study. We obtain several results regarding the properties of the graph, which are summarized as follows. The graph is a connected graph if and only if is prime and. If is connected, then diam and gr. Furthermore, is a Hamiltonian graph if is a prime number and.

Collaboration network of the authors

14 authors · 24 co-authorship links

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

  • 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 unknown3
Nughthoh Arfawi KurdhiAffiliation unknown2
Eka Widia RahayuAffiliation unknown1
Ririn SetiyowatiAffiliation unknown1
Zahra Febrilia RachmawatiAffiliation unknown1
Sutrima SutrimaAffiliation unknown1
Putri WulandariUniversitas Sulawesi Tenggara1
Zakia Nur Ramadhani PutriAffiliation unknown1
Ika Nur FitrianiThe University of Sydney1
Ade Safira SeptianyAffiliation unknown1
Bayu PurboutomoAffiliation 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) 
<oai_dc:dc xmlns="http://www.openarchives.org/OAI/2.0/" xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:oai_dc="http://www.openarchives.org/OAI/2.0/oai_dc/" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:schemaLocation="http://www.openarchives.org/OAI/2.0/oai_dc/  http://www.openarchives.org/OAI/2.0/oai_dc.xsd">
	<dc:title xml:lang="en-US">THE TRIPLE IDENTITY GRAPH OF THE RING Z_n</dc:title>
	<dc:creator>Kurniawan, Vika Yugi</dc:creator>
	<dc:creator>Ekasiwi, Chessa Fanny</dc:creator>
	<dc:creator>Wiyono, Santoso Budi</dc:creator>
	<dc:description xml:lang="en-US">Let &amp;nbsp;be a commutative ring with identity and &amp;nbsp;is an identity element of . The triple identity graph of the ring , represented by ), is an undirected simple graph with the vertex set . In , two different vertices &amp;nbsp;and &amp;nbsp;is called adjacent if there is an element such that and . The triple identity graph of the ring of integers modulo , represented by , is the subject of this study. We obtain several results regarding the properties of the graph , which are summarized as follows. The graph &amp;nbsp;is a connected graph if and only if &amp;nbsp;is prime and . If &amp;nbsp;is connected, then diam&amp;nbsp;and gr. Furthermore, &amp;nbsp;is a Hamiltonian graph if &amp;nbsp;is a prime number and .</dc:description>
	<dc:publisher xml:lang="en-US">PATTIMURA UNIVERSITY</dc:publisher>
	<dc:date>2025-09-01</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/17385</dc:identifier>
	<dc:identifier>10.30598/barekengvol19iss4pp2521-2530</dc:identifier>
	<dc:source xml:lang="en-US">BAREKENG: Jurnal Ilmu Matematika dan Terapan; Vol 19 No 4 (2025): BAREKENG: Journal of Mathematics and Its Application; 2521-2530</dc:source>
	<dc:source>2615-3017</dc:source>
	<dc:source>1978-7227</dc:source>
	<dc:source>10.30598/barekengvol19iss4year2025</dc:source>
	<dc:language>eng</dc:language>
	<dc:relation>https://ojs3.unpatti.ac.id/index.php/barekeng/article/view/17385/11067</dc:relation>
	<dc:rights xml:lang="en-US">Copyright (c) 2025 Vika Yugi Kurniawan, Chessa Fanny Ekasiwi; Santoso Budi Wiyono</dc:rights>
	<dc:rights xml:lang="en-US">http://creativecommons.org/licenses/by-sa/4.0</dc:rights>
</oai_dc:dc>