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Gutman, Sombor, and Harmonic Indices of Unit Graphs in The Integer Ring Modulo with A Specific Order

Jurnal Matematika, Statistika dan Komputasi · Vol. 21 No. 3 (2025) · pp. 725–738

DOI
10.20956/j.v21i3.43144
ISSN
2614-8811, 1858-1382
Published
2025-05-14
Publisher
Department of Mathematics, Hasanuddin University
Language
en
License
creativecommons.org/licenses/by/4.0

Abstract

The ring of integers modulo is an algebraic structure that plays an important role in various fields, such as number theory, cryptography, and number system modeling. This structure also has a strong connection to graph representation, especially in the formation of unit graphs. This research focuses on the analysis of unit graphs formed from modulo integer algebras of a certain order, which aims to formulate the general form of topological indices, namely Gutman, Sombor, Reduced Sombor, Average Sombor, and Harmonic. The research considers two cases: the ring of integer modulo and, where is an odd prime number. The results show that each index has a unique and specific mathematical pattern according to its unit graph order. These findings provide a deeper understanding of the topological and combinatorial properties of unit graphs, which may help in generalizing their topological indices.

Keywords

Collaboration network of the authors

31 authors · 70 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
Fariz MaulanaAffiliation unknown3
Muhammad Naoval HusniAffiliation unknown2
Ayes Malona SiboroAffiliation unknown2
Qurratul AiniAffiliation 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
M. AfdhaluzzikriAffiliation unknown1
Hena Rani BiswasAffiliation unknown1
Syamsul BahriAffiliation unknown1
Lailia AwalushaumiAffiliation unknown1
Bulqis Nebulla SyechahAffiliation 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
Na'imah HijriatiAffiliation unknown1
Sefti Fajriatul MusyarrofahAffiliation unknown1
Dimas IndrawadiAffiliation unknown1
Hazzirah Izzati HassimAffiliation 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">Gutman, Sombor, and Harmonic Indices of Unit Graphs in The Integer Ring Modulo with A Specific Order</dc:title>
	<dc:creator xml:lang="en">Pradana, Satriawan</dc:creator>
	<dc:creator xml:lang="en">Wardhana, I Gede Adhitya Wisnu</dc:creator>
	<dc:creator xml:lang="en">Satriyantara, Rio</dc:creator>
	<dc:subject xml:lang="en">Modulo Integer Ring</dc:subject>
	<dc:subject xml:lang="en">Unit Graph</dc:subject>
	<dc:subject xml:lang="en">Gutman Index</dc:subject>
	<dc:subject xml:lang="en">Sombor Index</dc:subject>
	<dc:subject xml:lang="en">Harmonic Index</dc:subject>
	<dc:description xml:lang="en">The ring of integers modulo  is an algebraic structure that plays an important role in various fields, such as number theory, cryptography, and number system modeling. This structure also has a strong connection to graph representation, especially in the formation of unit graphs. This research focuses on the analysis of unit graphs formed from modulo integer algebras of a certain order, which aims to formulate the general form of topological indices, namely Gutman, Sombor, Reduced Sombor, Average Sombor, and Harmonic. The research considers two cases: the ring of integer modulo  and , where  is an odd prime number. The results show that each index has a unique and specific mathematical pattern according to its unit graph order. These findings provide a deeper understanding of the topological and combinatorial properties of unit graphs, which may help in generalizing their topological indices.</dc:description>
	<dc:publisher xml:lang="en">Department of Mathematics, Hasanuddin University</dc:publisher>
	<dc:date>2025-05-14</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/43144</dc:identifier>
	<dc:identifier>10.20956/j.v21i3.43144</dc:identifier>
	<dc:source xml:lang="en">Jurnal Matematika, Statistika dan Komputasi; Vol. 21 No. 3 (2025): MAY 2025; 725-738</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/43144/12802</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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