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THE NON-COPRIME GRAPHS OF UPPER UNITRIANGULAR MATRIX GROUPS OVER THE RING OF INTEGER MODULO WITH PRIME ORDER AND THEIR TOPOLOGICAL INDICES

BAREKENG: Jurnal Ilmu Matematika dan Terapan · Vol. 19 No. 1 (2025) · pp. 547–556

DOI
10.30598/barekengvol19iss1pp547-556
ISSN
2615-3017, 1978-7227
Published
2025-01-13
Publisher
PATTIMURA UNIVERSITY
Language
eng
License
creativecommons.org/licenses/by-sa/4.0

Abstract

In its application graph theory is widely applied in various fields of science, including scheduling, transportation, industry, and structural chemistry, such as topological indexes. The study of graph theory is also widely applied as a form of representation of algebraic structures, including groups. One form of graph representation that has been studied is non-coprime graphs. The upper unitriangular matrix group is a form of group that can be represented in graph form. This group consists of upper unitriangular matrices, which are a special form of upper triangular matrix with entries in a ring R and all main diagonal entries have a value of one. In this research, we look for the form of a non-coprime graph from the upper unitriangular matrix group over a ring of prime modulo integers and several topological indexes, namely the Harmonic index, Wiener index, Harary index, and First Zagreb index. The findings of this research indicate that the structure of the graph and the general formula for the Harmonic index, Wiener index, Harary index, and First Zagreb index were successfully obtained.

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
Show as table
Co-authorOrganisationJoint articles
Muhammad Naoval HusniAffiliation unknown2
Ayes Malona SiboroAffiliation unknown2
Qurratul AiniAffiliation 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://ojs3.unpatti.ac.id/index.php/barekeng/oai, first harvested 5 Nov 2026, last seen 5 Nov 2026.
Original metadata (oai_dc) 
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	<dc:title xml:lang="en-US">THE NON-COPRIME GRAPHS OF UPPER UNITRIANGULAR MATRIX GROUPS OVER THE RING OF INTEGER MODULO WITH PRIME ORDER AND THEIR TOPOLOGICAL INDICES</dc:title>
	<dc:creator>Afdhaluzzikri, M.</dc:creator>
	<dc:creator>Wardhana, I Gede Adhitya Wisnu</dc:creator>
	<dc:creator>Maulana, Fariz</dc:creator>
	<dc:creator>Biswas, Hena Rani</dc:creator>
	<dc:description xml:lang="en-US">In its application graph theory is widely applied in various fields of science, including scheduling, transportation, industry, and structural chemistry, such as topological indexes. The study of graph theory is also widely applied as a form of representation of algebraic structures, including groups. One form of graph representation that has been studied is non-coprime graphs. The upper unitriangular matrix group is a form of group that can be represented in graph form. This group consists of upper unitriangular matrices, which are a special form of upper triangular matrix with entries in a ring R and all main diagonal entries have a value of one. In this research, we look for the form of a non-coprime graph from the upper unitriangular matrix group over a ring of prime modulo integers and several topological indexes, namely the Harmonic index, Wiener index, Harary index, and First Zagreb index. The findings of this research indicate that the structure of the graph and the general formula for the Harmonic index, Wiener index, Harary index, and First Zagreb index were successfully obtained.</dc:description>
	<dc:publisher xml:lang="en-US">PATTIMURA UNIVERSITY</dc:publisher>
	<dc:date>2025-01-13</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/14765</dc:identifier>
	<dc:identifier>10.30598/barekengvol19iss1pp547-556</dc:identifier>
	<dc:source xml:lang="en-US">BAREKENG: Jurnal Ilmu Matematika dan Terapan; Vol 19 No 1 (2025): BAREKENG: Journal of Mathematics and Its Application; 547-556</dc:source>
	<dc:source>2615-3017</dc:source>
	<dc:source>1978-7227</dc:source>
	<dc:source>10.30598/barekengvol19iss1year2025</dc:source>
	<dc:language>eng</dc:language>
	<dc:relation>https://ojs3.unpatti.ac.id/index.php/barekeng/article/view/14765/9566</dc:relation>
	<dc:rights xml:lang="en-US">Copyright (c) 2025 M. Afdhaluzzikri, I Gede Adhitya Wisnu Wardhana, Fariz Maulana, Hena Rani Biswas</dc:rights>
	<dc:rights xml:lang="en-US">http://creativecommons.org/licenses/by-sa/4.0</dc:rights>
</oai_dc:dc>