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Metric Dimension of Shackle Operation C_3 Cycle Graph

Dimensi Metrik dari Hasil Operasi Shackle Graf Siklus C_3

Jurnal Matematika, Statistika dan Komputasi · Vol. 19 No. 2 (2023) · pp. 317–322

DOI
10.20956/j.v19i2.22957
ISSN
2614-8811, 1858-1382
Published
2023-01-05
Publisher
Department of Mathematics, Hasanuddin University
Language
en
License
creativecommons.org/licenses/by/4.0

Abstract

English

Let G be a connected graph and W be a ordered vertices subset on a connected graph. The set W is called resolving set for G if every vertex on graph G has distinct representation of W. A resolving set containing a minimum number of vertices is called resolving set minimum or basis for G and the cardinality of resolving set is the metric dimension on graph G, denoted by dim(G). In the thesis discusses about metric dimensions of shackle operation C3 cycle graph, dim(Shack(C31,C32,…,C3k:v31=v12,v32=v13,…,v3k-1=v1k ))=2 for k>=2. To proof this results, we was used mathematical induction method.

Bahasa Indonesia

Misalkan G adalah graf terhubung dan W adalah sub himpunan titik terurut pada graf terhubung G. Himpunan W disebut himpunan pembeda pada G jika untuk setiap titik pada graf G memiliki representasi jarak yang berbeda tehadap W. Himpunan pembeda dengan banyak anggota minimum disebut himpunan pembeda minimum atau basis dari G dan kardinalitas himpunan tersebut adalah dimensi metrik pada graf G, dinotasikan dengan dim(G). Dalam makalah ini dibahas mengenai dimensi metrik hasil operasi shackle graf siklus C3, dim(Shack(C31,C32,…,C3k:v31=v12,v32=v13,…,v3k-1=v1k ))=2 untuk k>=2. Metode yang digunakan dalam membuktikan hasil tersebut adalah induksi matematika.

Keywords

Collaboration network of the authors

40 authors · 93 co-authorship links · 4 across different organisations · showing the 40 most connected

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

  • Universitas Halu Oleo
  • Telkom University
  • Hasanuddin 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 unknown3
Ahmad Syukur DamingAffiliation unknown3
Nur ErawatiAffiliation unknown2
Nurdin HindingAffiliation unknown2
Loeky HaryantoAffiliation unknown2
Ari Moesriami BarmawiTelkom University1
Rimba HamidUniversitas Halu Oleo1
Nana SumarnaUniversitas Halu Oleo1
La Ili La IliAffiliation unknown1
Aris BadaraUniversitas Halu Oleo1
Amirudin RahimAffiliation unknown1
Ida SriwatyAffiliation unknown1
Waode SuarniAffiliation unknown1
Saleh SalehAffiliation unknown1
La Ndia La NdiaAffiliation unknown1
Andi SadapottoAffiliation unknown1
Haidir JibranAffiliation unknown1
Irfan Hakim MaridiAffiliation unknown1
Amanda Putri sAffiliation unknown1
Dhea Rizky MalindaAffiliation unknown1
Denaya Mutiara SalsaAffiliation unknown1
Dila Amelia PutriAffiliation unknown1
Vanessa J.A. PandelakiAffiliation unknown1
Jeriko GormantaraAffiliation unknown1
Hanni GarminiaAffiliation unknown1
Evan RamdanAffiliation unknown1
Afriani AfrianiAffiliation unknown1
Qharnida KharianiAffiliation unknown1
Hasmawati BasirAffiliation unknown1
winda aritonangAffiliation unknown1
Armin LawiHasanuddin University1
Nurhidayah NurhidayahUniversitas Halu Oleo1
Safriadi SafriadiAffiliation unknown1
Mawardi BahriAffiliation unknown1
Yudhiyanto SupriadiAffiliation unknown1
Aidah Nabilah AnwarAffiliation unknown1
Haspika HaspikaAffiliation 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">Metric Dimension of Shackle Operation C_3 Cycle Graph</dc:title>
	<dc:title xml:lang="id">Dimensi Metrik dari Hasil Operasi Shackle Graf Siklus C_3</dc:title>
	<dc:creator xml:lang="en">Fachrunnisa, St. Munieroh  </dc:creator>
	<dc:creator xml:lang="en">Hasmawati, Hasmawati</dc:creator>
	<dc:creator xml:lang="en">Amir, Amir Kamal </dc:creator>
	<dc:subject xml:lang="en">Metric Dimension</dc:subject>
	<dc:subject xml:lang="en">Shackle Operation</dc:subject>
	<dc:subject xml:lang="en">Cycle Graph</dc:subject>
	<dc:subject xml:lang="id">Dimensi Metrik</dc:subject>
	<dc:subject xml:lang="id">Operasi Shackle</dc:subject>
	<dc:subject xml:lang="id">Graf Siklus</dc:subject>
	<dc:description xml:lang="en">Let G be a connected graph and W&amp;nbsp; be a ordered vertices subset on a connected graph . The set W is called resolving set for G if every vertex on graph G has distinct representation of W. A resolving set containing a minimum number of vertices is called resolving set minimum or basis for G and the cardinality of resolving set is the metric dimension on graph G,&amp;nbsp; denoted by dim(G).&amp;nbsp; In the thesis discusses about metric dimensions of shackle operation C3 cycle graph, dim(Shack(C31,C32,…,C3k:v31=v12,v32=v13,…,v3k-1=v1k ))=2 for k&amp;gt;=2 . To proof this results, we was used mathematical induction method.</dc:description>
	<dc:description xml:lang="id">Misalkan G adalah graf terhubung dan W adalah sub himpunan titik terurut pada graf terhubung G. Himpunan W disebut himpunan pembeda pada G jika untuk setiap titik pada graf G memiliki representasi jarak yang berbeda tehadap W. Himpunan pembeda dengan banyak anggota minimum disebut himpunan pembeda minimum atau basis dari G dan kardinalitas himpunan tersebut adalah dimensi metrik pada graf G, dinotasikan dengan dim(G). Dalam makalah ini dibahas mengenai dimensi metrik hasil operasi shackle graf siklus C3, dim(Shack(C31,C32,…,C3k:v31=v12,v32=v13,…,v3k-1=v1k ))=2&amp;nbsp;untuk k&amp;gt;=2. Metode yang digunakan dalam membuktikan hasil tersebut adalah induksi matematika.</dc:description>
	<dc:publisher xml:lang="en">Department of Mathematics, Hasanuddin University</dc:publisher>
	<dc:date>2023-01-05</dc:date>
	<dc:type>info:eu-repo/semantics/article</dc:type>
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	<dc:format>application/pdf</dc:format>
	<dc:identifier>https://journal.unhas.ac.id/index.php/jmsk/article/view/22957</dc:identifier>
	<dc:identifier>10.20956/j.v19i2.22957</dc:identifier>
	<dc:source xml:lang="en">Jurnal Matematika, Statistika dan Komputasi; Vol. 19 No. 2 (2023): JANUARY 2023; 317-322</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/22957/9154</dc:relation>
	<dc:relation>10.20956/j.v19i2.22957.g9154</dc:relation>
	<dc:rights xml:lang="en">Copyright (c) 2023 Author and publisher</dc:rights>
	<dc:rights xml:lang="en">https://creativecommons.org/licenses/by/4.0</dc:rights>
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