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Fisrt Zagreb, Gutman, and Wiener Index of The Non-Coprime Graph for Dihedral Group

Jurnal Matematika, Statistika dan Komputasi · Vol. 23 No. 1 (2026) · pp. 1–6

DOI
10.20956/sqqdm542
ISSN
2614-8811, 1858-1382
Published
2026-09-15
Publisher
Department of Mathematics, Hasanuddin University
Language
en
License
creativecommons.org/licenses/by/4.0

Abstract

This study investigates the structure of non-coprime graphs derived from the dihedral groups of prime power order using approaches from graph theory and group theory. In molecular representation and pure mathematics, graphs serve a tool to illustrate the internal structure of systems through topological indices. A non-coprime graph is a graph formed by connecting two distinct vertices if the greatest common divisor (GCD) of their orders is not equal to one, meaning the two elements are not coprime. The primary focus of this research is to derive general formulas for the first Zagreb index, the Gutman index, and the Wiener index of non-coprime graphs constructed from the dihedral group ​. For the first Zagreb index, the cases and are considered, where is a prime number and is a positive integer. Meanwhile, for the Gutman and Wiener indices, the study focuses on the case, with as a positive integer. This research produces explicit formulas for the first Zagreb index, Gutman index, and Wiener index of the corresponding non-coprime graphs.

Keywords

Collaboration network of the authors

28 authors · 64 co-authorship links

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  • Universitas Pendidikan Ganesha
  • Affiliation unknown
  • Different organisations
  • Same organisation
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Co-authorOrganisationJoint articles
Muhammad Naoval HusniAffiliation unknown2
Ayes Malona SiboroAffiliation unknown2
Qurratul AiniAffiliation unknown2
M. AfdhaluzzikriAffiliation unknown2
Hena Rani BiswasAffiliation unknown2
Hanna SyafitriAffiliation unknown1
Abdul Gazir SyarifudinAffiliation unknown1
Dewi Santri RamdaniAffiliation unknown1
Zatta Yumni AwanisAffiliation unknown1
Lalu Riski Wirendra PutraAffiliation unknown1
Zata Yumni AwanisAffiliation unknown1
Salwa SalwaAffiliation unknown1
Sarwa HitaAffiliation unknown1
Nguyen Dang Hoa NghiemAffiliation unknown1
Ni Komang Tri DharmayaniAffiliation unknown1
Putu Kartika DewiUniversitas Pendidikan Ganesha1
I Nengah SupartaAffiliation unknown1
Baiq Rika Ayu FebriliaAffiliation unknown1
M FauzulAffiliation unknown1
Putri Kurnia ChairunnisaAffiliation unknown1
Satriawan PradanaAffiliation unknown1
Rio SatriyantaraAffiliation unknown1
Na'imah HijriatiAffiliation unknown1
Sefti Fajriatul MusyarrofahAffiliation 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">Fisrt Zagreb, Gutman, and Wiener Index of The Non-Coprime Graph for Dihedral Group </dc:title>
	<dc:creator xml:lang="en">Indrawadi, Dimas</dc:creator>
	<dc:creator xml:lang="en">Wardhana, I Gede Adhitya Wisnu</dc:creator>
	<dc:creator xml:lang="en">Hassim, Hazzirah Izzati</dc:creator>
	<dc:creator xml:lang="en">Maulana, Fariz</dc:creator>
	<dc:subject xml:lang="en">non-coprime graph</dc:subject>
	<dc:subject xml:lang="en">dihedral group</dc:subject>
	<dc:subject xml:lang="en">first Zagreb index</dc:subject>
	<dc:subject xml:lang="en">Gutman index</dc:subject>
	<dc:subject xml:lang="en">Wiener index</dc:subject>
	<dc:description xml:lang="en">This study investigates the structure of non-coprime graphs derived from the dihedral groups of prime power order using approaches from graph theory and group theory. In molecular representation and pure mathematics, graphs serve a tool to illustrate the internal structure of systems through topological indices. A non-coprime graph is a graph formed by connecting two distinct vertices if the greatest common divisor (GCD) of their orders is not equal to one, meaning the two elements are not coprime. The primary focus of this research is to derive general formulas for the first Zagreb index, the Gutman index, and the Wiener index of non-coprime graphs constructed from the dihedral group ​. For the first Zagreb index, the cases &amp;nbsp;and &amp;nbsp;are considered, where &amp;nbsp;is a prime number and &amp;nbsp;is a positive integer. Meanwhile, for the Gutman and Wiener indices, the study focuses on the case, with &amp;nbsp;as a positive integer. This research produces explicit formulas for the first Zagreb index, Gutman index, and Wiener index of the corresponding non-coprime graphs.</dc:description>
	<dc:publisher xml:lang="en">Department of Mathematics, Hasanuddin University</dc:publisher>
	<dc:date>2026-09-15</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/48964</dc:identifier>
	<dc:identifier>10.20956/sqqdm542</dc:identifier>
	<dc:source xml:lang="en">Jurnal Matematika, Statistika dan Komputasi; Vol. 23 No. 1 (2026): September 2026; 1-6</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/48964/14999</dc:relation>
	<dc:rights xml:lang="en">Copyright (c) 2026 Jurnal Matematika, Statistika dan Komputasi</dc:rights>
	<dc:rights xml:lang="en">https://creativecommons.org/licenses/by/4.0</dc:rights>
</oai_dc:dc>