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Hyper-Wiener and Harary Indices of The Line Graph of Zero Divisor Graph For Integer Modulo Ring

Jurnal Matematika, Statistika dan Komputasi · Vol. 22 No. 3 (2026) · pp. 540–545

DOI
10.20956/j.v22i3.48758
ISSN
2614-8811, 1858-1382
Published
2026-05-14
Publisher
Department of Mathematics, Hasanuddin University
Language
en
License
creativecommons.org/licenses/by/4.0

Abstract

This paper studies the line graph of the zero divisor graph of the ring Z_(P^n ), where p is a prime and n is a natural number. The main objective is to compute closed formulas for the Hyper–Wiener and Harary indices of the line graph L(〖ΓZ〗_(P^n ) ) and to analyze their relationship with the first Zagreb index of the original graph ΓZ_(P^n ). The results establish connections between structural properties of the zero divisor graph and those of its corresponding line graph, offering a deeper understanding of interactions among degree-based and distance-based topological indices.

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
  • Affiliation unknown
  • Thicker line = more joint articles · bigger circle = more articles
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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
Dimas IndrawadiAffiliation unknown2
Hazzirah Izzati HassimAffiliation 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">Hyper-Wiener and Harary Indices of The Line Graph of Zero Divisor Graph For Integer Modulo Ring</dc:title>
	<dc:creator xml:lang="en">Maulana, Fariz</dc:creator>
	<dc:creator xml:lang="en">Wardhana, I Gede Adhitya Wisnu</dc:creator>
	<dc:subject xml:lang="en">Line Graph</dc:subject>
	<dc:subject xml:lang="en">Zero Divisor Graph</dc:subject>
	<dc:subject xml:lang="en">Integer modulo ring</dc:subject>
	<dc:subject xml:lang="en">Hyper Wiener index</dc:subject>
	<dc:subject xml:lang="en">Harary index</dc:subject>
	<dc:subject xml:lang="en">First Zagreb index</dc:subject>
	<dc:description xml:lang="en">This paper studies the line graph of the zero divisor graph of the ring Z_(P^n ), where p is a prime and n is a natural number. The main objective is to compute closed formulas for the Hyper–Wiener and Harary indices of the line graph L(〖ΓZ〗_(P^n ) ) and to analyze their relationship with the first Zagreb index of the original graph ΓZ_(P^n ). The results establish connections between structural properties of the zero divisor graph and those of its corresponding line graph, offering a deeper understanding of interactions among degree-based and distance-based topological indices.</dc:description>
	<dc:publisher xml:lang="en">Department of Mathematics, Hasanuddin University</dc:publisher>
	<dc:date>2026-05-14</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/48758</dc:identifier>
	<dc:identifier>10.20956/j.v22i3.48758</dc:identifier>
	<dc:source xml:lang="en">Jurnal Matematika, Statistika dan Komputasi; Vol. 22 No. 3 (2026): May 2026; 540-545</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/48758/14408</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>