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Szeged Index and Padmakar-Ivan Index of Nilpotent Graph of Integer Modulo Ring with Prime Power Order

Indeks Szeged dan Indeks Padmakar-Ivan pada Graf Nilpoten pada Gelanggang Bilangan Bulat Modulo Orde Prima Berpangkat

Jurnal Matematika, Statistika dan Komputasi · Vol. 20 No. 2 (2023) · pp. 332–339

DOI
10.20956/j.v20i2.31418
ISSN
2614-8811, 1858-1382
Published
2023-12-24
Publisher
Department of Mathematics, Hasanuddin University
Language
en
License
creativecommons.org/licenses/by/4.0

Abstract

English

Recently, graphs have started to be used to represent a finite ring. Nikmehr and Khojasteh in the article defined the nilpotent graph of a ring. Denoted, is a graph with the set of vertices being all the elements in the ring Two vertices and are adjacent if and only if is nilpotent elements in the ring. Topological index is a field that discusses graph structure based on the degree of each vertex of a graph and the distance between vertices. In this study, the author will gives the general formula of the Szeged index and Padmakar-Ivan index of the nilpotent graph graph of the modulo ring with prime power order. The result of this research is a general formula for the topological indices of nilpotent graphs of the integer modulo ring, called the Szeged index and the Padmakar-Ivan index.

Bahasa Indonesia

Dalam beberapa tahun terakhir, graf mulai digunakan untuk merepresentasikan suatu gelanggang hingga. Nikmehr and Khojasteh dalam artikel mendefinisikan graf nipolten dari gelanggang R, disimbolkan TR, adalah graf dengan himpunan simpul adalah semua unsur di gelanggang R. Dua simpul x dan y berbeda bertetangga jika dan hanya jika xy merupakan unsur nilpoten pada gelangggang R. Indeks topologi adalah salah satu bidang yang membahas mengenai struktur graf berdasarkan pada jarak dan derajat dari setiap simpul, dalam penelitian ini penulis akan membahas perumuman indeks Szeged dan Index Padmakar-Ivan dari graf nilpoten dari gelanggang modulo dengan orde prima berpangkat. Hasil dari penelitian ini adalah rumus umum untuk indeks topologi graf nilpoten dari gelanggang modulo yaitu indeks Szeged dan indeks Padmakar-Ivan

Keywords

Collaboration network of the authors

35 authors · 80 co-authorship links · 1 across different organisations

Hover or tap a name to highlight its co-authors. Double-click to open the author's page.

  • Universitas Pendidikan Ganesha
  • Universitas Halu Oleo
  • Universitas Jember
  • Affiliation unknown
  • Different organisations
  • Same organisation
  • Affiliation unknown
  • Thicker line = more joint articles · bigger circle = more articles
Show as table
Co-authorOrganisationJoint articles
Fariz MaulanaAffiliation unknown3
Ayes Malona SiboroAffiliation unknown3
Qurratul AiniAffiliation unknown3
Hanna SyafitriAffiliation unknown2
Abdul Gazir SyarifudinAffiliation unknown2
I Gusti Ayu Agung Intan Ananda Suari YudiasaUniversitas Pendidikan Ganesha1
Ni Made Sri MertasariUniversitas Pendidikan Ganesha1
I Made ArdanaUniversitas Pendidikan Ganesha1
Gusti Ayu MahayuktiUniversitas Pendidikan Ganesha1
Dewi Santri RamdaniAffiliation unknown1
Zatta Yumni AwanisAffiliation unknown1
Lalu Riski Wirendra PutraAffiliation unknown1
Zata Yumni AwanisAffiliation unknown1
Salwa SalwaAffiliation unknown1
Dafik DafikUniversitas Jember1
ROBIATUL ADAWIYAHUniversitas Halu Oleo1
Muhammad Ilham Nurfaizi AnnadhifiAffiliation unknown1
M. AfdhaluzzikriAffiliation unknown1
Hena Rani BiswasAffiliation unknown1
Sarwa HitaAffiliation unknown1
Nguyen Dang Hoa NghiemAffiliation unknown1
Ni Komang Tri DharmayaniAffiliation 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
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">Szeged Index and Padmakar-Ivan Index of Nilpotent Graph of Integer Modulo Ring with Prime Power Order </dc:title>
	<dc:title xml:lang="id">Indeks Szeged dan Indeks Padmakar-Ivan pada Graf Nilpoten pada Gelanggang Bilangan Bulat Modulo Orde Prima Berpangkat</dc:title>
	<dc:creator xml:lang="en">Husni, Muhammad Naoval</dc:creator>
	<dc:creator xml:lang="en">Wardhana, I Gede Adhitya Wisnu</dc:creator>
	<dc:creator xml:lang="en">Dewi, Putu Kartika</dc:creator>
	<dc:creator xml:lang="en">Suparta, I Nengah</dc:creator>
	<dc:subject xml:lang="en">nilpotent graph</dc:subject>
	<dc:subject xml:lang="en">Szedge Index</dc:subject>
	<dc:subject xml:lang="en">Padmakar-Ivan index</dc:subject>
	<dc:subject xml:lang="id">graf nilpoten</dc:subject>
	<dc:subject xml:lang="id">indeks Szeged</dc:subject>
	<dc:subject xml:lang="id">indeks Padmakar-Ivan</dc:subject>
	<dc:description xml:lang="en">Recently, graphs have started to be used to represent a finite ring. Nikmehr and  Khojasteh in the article  defined the nilpotent graph of a ring . Denoted , is a graph with the set of vertices being all the elements in the ring  Two vertices  and  are adjacent if and only if  is nilpotent elements in the ring . Topological index is a field that discusses graph structure based on the degree of each vertex of a graph and the distance between vertices.  In this study, the author will gives the general formula of the Szeged index and Padmakar-Ivan index of the nilpotent graph graph of the modulo ring with prime power order. The result of this research is a general formula for the topological indices of nilpotent graphs of the integer modulo ring, called the Szeged index and the Padmakar-Ivan index.</dc:description>
	<dc:description xml:lang="id">Dalam beberapa tahun terakhir, graf mulai digunakan untuk merepresentasikan suatu gelanggang hingga. Nikmehr and&amp;nbsp; Khojasteh dalam artikel mendefinisikan graf nipolten dari gelanggang R, disimbolkan TR, adalah graf dengan himpunan simpul adalah semua unsur di gelanggang R. Dua simpul x dan y berbeda bertetangga jika dan hanya jika xy merupakan unsur nilpoten pada gelangggang R. Indeks topologi adalah salah satu bidang yang membahas mengenai struktur graf berdasarkan pada jarak dan derajat dari setiap simpul, dalam penelitian ini penulis akan membahas perumuman indeks Szeged dan Index Padmakar-Ivan dari graf nilpoten dari gelanggang modulo dengan orde prima berpangkat. Hasil dari penelitian ini adalah rumus umum untuk indeks topologi graf nilpoten dari gelanggang modulo yaitu indeks Szeged dan indeks Padmakar-Ivan</dc:description>
	<dc:publisher xml:lang="en">Department of Mathematics, Hasanuddin University</dc:publisher>
	<dc:date>2023-12-24</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/31418</dc:identifier>
	<dc:identifier>10.20956/j.v20i2.31418</dc:identifier>
	<dc:source xml:lang="en">Jurnal Matematika, Statistika dan Komputasi; Vol. 20 No. 2 (2024): JANUARY 2024; 332-339</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/31418/10946</dc:relation>
	<dc:relation>10.20956/j.v20i2.31418.g10946</dc:relation>
	<dc:rights xml:lang="en">Copyright (c) 2023 Author and publisher</dc:rights>
	<dc:rights xml:lang="en">https://creativecommons.org/licenses/by/4.0</dc:rights>
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