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THE PARTITION DIMENSION OF CYCLE BOOKS GRAPH B_(m,n) WITH A COMMON PATH P_2

BAREKENG: Jurnal Ilmu Matematika dan Terapan · Vol. 19 No. 2 (2025) · pp. 791–804

DOI
10.30598/barekengvol19iss2pp791-804
ISSN
2615-3017, 1978-7227
Published
2025-04-01
Publisher
PATTIMURA UNIVERSITY
Language
eng
License
creativecommons.org/licenses/by-sa/4.0

Abstract

Suppose is a connected graph with elements of a set of vertices denoted by and a subset of. The distance between and is the shortest distance to every vertex in. Let be a partition of, where each subset belongs to. The representation of a vertex with respect to is defined as the set of distances from to each vertex in. If each representation of each vertex of is different, then the partition is called the resolving partition of, and the partition dimension is the smallest integer such that has a resolving partition with members. In this research, we show the partition dimensions of the cycle books graph. Cycle books graph is a graph consisting of copies of a cycle with a common path. The partition dimension of the cycle books graph for and is shown.

Collaboration network of the authors

26 authors · 77 co-authorship links · 11 across different organisations

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  • Universitas Jambi
  • Institut Teknologi Del
  • Institut Teknologi Sepuluh Nopember
  • The University of Adelaide
  • Affiliation unknown
  • Different organisations
  • Same organisation
  • Affiliation unknown
  • Thicker line = more joint articles · bigger circle = more articles
Show as table
Co-authorOrganisationJoint articles
Dwi Agus KurniawanUniversitas Jambi7
Astalini AstaliniAffiliation unknown5
Wawan KurniawanThe University of Adelaide2
Maison MaisonAffiliation unknown1
Diyen ParamithaAffiliation unknown1
Ana MuliyanaInstitut Teknologi Del1
Asido SaragihInstitut Teknologi Del1
Darmaji DarmajiInstitut Teknologi Sepuluh Nopember1
Kamid KamidUniversitas Jambi1
Astalini AstaliniUniversitas Jambi1
Darmaji DarmajiUniversitas Jambi1
Elza TrianiUniversitas Jambi1
Wita Ardina PutriAffiliation unknown1
Feliza Paramitha SinagaAffiliation unknown1
Jufrida JufridaAffiliation unknown1
Weni Angra MayaAffiliation unknown1
M. HidayatAffiliation unknown1
Nugroho KurniawanAffiliation unknown1
Linda Zaenati Nur FaridaAffiliation unknown1
Irdianti IrdiantiAffiliation unknown1
Rahmat PerdanaAffiliation unknown1
Kuswanto KuswantoAffiliation unknown1
Muhammad IkhlasAffiliation unknown1
Ririn MelsayantiAffiliation 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 8 Nov 2026.
Original metadata (oai_dc) 
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	<dc:title xml:lang="en-US">THE PARTITION DIMENSION OF CYCLE BOOKS GRAPH B_(m,n) WITH A COMMON PATH P_2</dc:title>
	<dc:creator>Santoso, Jaya</dc:creator>
	<dc:creator>Darmaji, Darmaji</dc:creator>
	<dc:description xml:lang="en-US">Suppose  &amp;nbsp;is a connected graph with  &amp;nbsp;elements of a set of vertices  &amp;nbsp;denoted by  &amp;nbsp;and  &amp;nbsp;a subset of  . The distance between  &amp;nbsp;and  &amp;nbsp;is the shortest distance  &amp;nbsp;to every vertex  &amp;nbsp;in  . Let  &amp;nbsp;be a partition of  , where each subset  &amp;nbsp;belongs to  . The representation of a vertex  &amp;nbsp;with respect to  &amp;nbsp;is defined as the set of distances from  &amp;nbsp;to each vertex in  . If each representation of each vertex of  &amp;nbsp;is different, then the partition  &amp;nbsp;is called the resolving partition of  , and the partition dimension  &amp;nbsp;is the smallest integer  &amp;nbsp;such that  &amp;nbsp;has a resolving partition with  &amp;nbsp;members. In this research, we show the partition dimensions of the cycle books graph  . Cycle books graph  &amp;nbsp;is a graph consisting of  &amp;nbsp;copies of a cycle with a common path  . The partition dimension of the cycle books graph  &amp;nbsp;for  &amp;nbsp;and  &amp;nbsp;is shown.</dc:description>
	<dc:publisher xml:lang="en-US">PATTIMURA UNIVERSITY</dc:publisher>
	<dc:date>2025-04-01</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/14261</dc:identifier>
	<dc:identifier>10.30598/barekengvol19iss2pp791-804</dc:identifier>
	<dc:source xml:lang="en-US">BAREKENG: Jurnal Ilmu Matematika dan Terapan; Vol 19 No 2 (2025): BAREKENG: Journal of Mathematics and Its Application; 791-804</dc:source>
	<dc:source>2615-3017</dc:source>
	<dc:source>1978-7227</dc:source>
	<dc:source>10.30598/barekengvol19iss2year2025</dc:source>
	<dc:language>eng</dc:language>
	<dc:relation>https://ojs3.unpatti.ac.id/index.php/barekeng/article/view/14261/9894</dc:relation>
	<dc:rights xml:lang="en-US">Copyright (c) 2025 Jaya Santoso, Darmaji Darmaji</dc:rights>
	<dc:rights xml:lang="en-US">http://creativecommons.org/licenses/by-sa/4.0</dc:rights>
</oai_dc:dc>