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Partition Dimension of the Sum Product of Complete Graph K_1 and Saw Graph GR_n

Jurnal Matematika, Statistika dan Komputasi · Vol. 21 No. 2 (2025) · pp. 573–582

DOI
10.20956/j.v21i2.32376
ISSN
2614-8811, 1858-1382
Published
2025-01-12
Publisher
Department of Mathematics, Hasanuddin University
Language
en
License
creativecommons.org/licenses/by/4.0

Abstract

Let and let denote the distance between dan. The distance of to a subset is denote by where Furthermore, suppose is an ordered partition with for then the representation of a vertex with respect to is the ordered k-tuple dinoted by. The partition is called a distinguishing partition of if for every. A distinguishing partition of with the smallest cardinality is called the minimum distinguishing partition of, and its cardinality is called the partition dimension of. The purpose of this study is to determine the partition dimension of the join graph and. By applying the concepts of equivalent vertices and vertices of the same level, it is shown that the partition dimension of the graph is where is a natural number.

Keywords

Collaboration network of the authors

30 authors · 68 co-authorship links

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  • State University of Makassar
  • Telkom University
  • Affiliation unknown
  • Different organisations
  • Same organisation
  • Affiliation unknown
  • Thicker line = more joint articles · bigger circle = more articles
Show as table
Co-authorOrganisationJoint articles
Budi NurwahyuAffiliation unknown4
Muh NurAffiliation unknown4
Islamiyah AbbasAffiliation unknown2
Hasmawati BasirAffiliation unknown2
Aswad Hariri MangalaengAffiliation unknown2
Edy Saputra RusdiAffiliation unknown1
A. Muh. Amil SiddikAffiliation unknown1
Muhammad Ardiansyah AsrifahAffiliation unknown1
Nur Hilal A. SyahrirAffiliation unknown1
Aidawayati RangkutiAffiliation unknown1
Wahyudi RusdiAffiliation unknown1
EDY SAPUTRA RUSDIAffiliation unknown1
Khaeruddin KhaeruddinState University of Makassar1
Meriam MeriamAffiliation unknown1
Faisal FaisalAffiliation unknown1
Muh. Ali ImranAffiliation unknown1
Afif Budi Andy BAffiliation unknown1
Muhammad Nur HidayatAffiliation unknown1
Jeffry KusumaAffiliation unknown1
Salsabila AmmariAffiliation unknown1
Indi Ria Al KadryAffiliation unknown1
Hasmawati HasmawatiTelkom University1
Haspika HaspikaAffiliation unknown1
Ervie Yuniarti Astika Mustafaputri YuniartiAffiliation unknown1
Heryati Nur Fatimah SariAffiliation unknown1
Saskia Nurul JannahAffiliation unknown1
Cindy CindyAffiliation 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://journal.unhas.ac.id/index.php/jmsk/oai, first harvested 5 Nov 2026, last seen 5 Nov 2026.
Original metadata (oai_dc) 
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	<dc:title xml:lang="en">Partition Dimension of the Sum Product of Complete Graph K_1 and Saw Graph GR_n</dc:title>
	<dc:creator xml:lang="en">Massalesse, Jusmawati</dc:creator>
	<dc:creator xml:lang="en">Saputra, Dermawan</dc:creator>
	<dc:creator xml:lang="en">Aris, Naimah</dc:creator>
	<dc:subject xml:lang="en">partition dimension</dc:subject>
	<dc:subject xml:lang="en">sum product of graph</dc:subject>
	<dc:subject xml:lang="en">complete graph</dc:subject>
	<dc:subject xml:lang="en">saw graph</dc:subject>
	<dc:subject xml:lang="en">equivalent vertices</dc:subject>
	<dc:subject xml:lang="en">level vertices</dc:subject>
	<dc:description xml:lang="en">Let   and  let denote the distance between dan . The distance of  to a subset  is denote by  where  Furthermore, suppose   is an ordered partition with  for  then the representation of a vertex  with respect to  is the ordered k-tuple dinoted by . The partition  is called a distinguishing partition of  if  for every .   A distinguishing partition of  with the smallest cardinality is called the minimum distinguishing partition of , and its cardinality is called the partition dimension of . The purpose of this study is to determine the partition dimension of the join graph  and . By applying the concepts of equivalent vertices and vertices of the same level, it is shown that the partition dimension of the graph  is  where  is a natural number.</dc:description>
	<dc:publisher xml:lang="en">Department of Mathematics, Hasanuddin University</dc:publisher>
	<dc:date>2025-01-12</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://journal.unhas.ac.id/index.php/jmsk/article/view/32376</dc:identifier>
	<dc:identifier>10.20956/j.v21i2.32376</dc:identifier>
	<dc:source xml:lang="en">Jurnal Matematika, Statistika dan Komputasi; Vol. 21 No. 2 (2025): JANUARY 2025; 573-582</dc:source>
	<dc:source>2614-8811</dc:source>
	<dc:source>1858-1382</dc:source>
	<dc:language>en</dc:language>
	<dc:relation>https://journal.unhas.ac.id/index.php/jmsk/article/view/32376/12453</dc:relation>
	<dc:rights xml:lang="en">Copyright (c) 2025 Jurnal Matematika, Statistika dan Komputasi</dc:rights>
	<dc:rights xml:lang="en">https://creativecommons.org/licenses/by/4.0</dc:rights>
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