INDEKS WIENER PADA GRAF KOPRIMA PRIMA DARI GRUP BILANGAN BULAT MODULO
DOI:
https://doi.org/10.25077/jmua.15.2.249-258.2026Keywords:
graf bipartit, graf lengkap, subgrafAbstract
Graf Koprima Prima merupakan graf yang mana sebarang dua simpul berbeda dikatakan bertetangga jika dan hanya jika Faktor Persekutuan terbesar (FPB) dari order kedua simpul sama dengan 1 atau prima. Penelitian ini bertujuan untuk mengkaji subgraf serta rumus umum dari indeks Wiener dan Hyper-Wiener pada graf koprima prima dari grup bilangan bulat. Dari penelitian ini didapatkan bahwa subgraf yang terbentuk adalah graf lengkap dan bipartit. Selain itu, diperoleh juga rumus umum indeks Wiener dan Hyper-Wiener. Lebih jauh, nilai dari indeks Hyper-Wiener kurang dari dua kali indeks Wiener.References
M. Bello, N. Muhainiah, M. Ali, and N. A. Zulkifli, “The Wiener And Zagreb Indices Of The The Wiener And Zagreb Indices,†J. Crit. Rev., vol. 7, no. 16, pp. 896–901, 2020.
X. Ma, H. Wei, and L. Yang, “The coprime graph of a group,†Int. J. Gr. Theory, vol. 3, no. 2, pp. 13–23, 2014, doi: https://doi.org/10.22108/ijgt.2014.4363.
B. Zainun Yatin, M. R. Gayatri, I. G. A. W. Wardhana, and B. D. Prayanti, “Indeks Hyper-Wiener Dan Indeks Padmakar-Ivan Dari Graf Koprima Dari Grup Dihedral,†J. Ris. dan Apl. Mat., vol. 07, no. 02, pp. 138–147, 2023, doi: https://doi.org/10.26740/jram.v7n2.p138-147.
A. Abdurahim, Z. Y. Awanis, B. N. Syechah, and S. Syaharuddin, “The Topological Indices of Coprime Graph for Integer Module Group,†J. Difer., vol. 6, no. 2, pp. 141–147, 2024, doi: 10.35508/jd.v6i2.14816.
M. R. Gayatri, R. Fadhilah, S. T. Lestari, L. F. Pratiwi, A. Abdurahim, and I. G. A. W. Wardhana, “Topology Index of the Coprime Graph for Dihedral Group of Prime Power Order,†J. Difer., vol. 5, no. 2, pp. 126–134, 2023, doi: 10.35508/jd.v5i2.12462.
E. Y. Asmarani, S. T. Lestari, D. Purnamasari, A. G. Syarifudin, S. Salwa, and I. G. A. W. Wardhana, “The First Zagreb Index, The Wiener Index, and The Gutman Index of The Power of Dihedral Group,†CAUCHY J. Mat. Murni dan Apl., vol. 7, no. 4, pp. 513–520, 2023, doi: https://dx.doi.org/10.18860/ca.v7i4.16991.
M. Ghorbani, M. R. Darafsheh, and P. Yousefzadeh, “On the Prime Graph of a Finite Group,†Miskolc Math. Notes, vol. 22, no. 1, pp. 201–210, 2021, doi: 10.18514/MMN.2021.1668.
A. Adhikari and S. Banerjee, “Prime coprime graph of a finite group,†Novi Sad J. Math., vol. 52, no. 2, pp. 41–59, 2022, doi: 10.30755/NSJOM.11151.
N. Cohen, D. Dimitrov, R. Krakovski, R. Skrekovski, and V. Vukašinović, “On Wiener index of graphs and their line graphs,†MATCH Commun. Math. Comput. Chem., vol. 64, no. 3, pp. 683–698, 2010.
L. Feng, W. Liu, G. Yu, and S. Li, “The hyper-Wiener index of graphs with given bipartition,†Util. Math., vol. 95, no. December 2015, pp. 23–32, 2014.
Downloads
Published
Issue
Section
License
Copyright (c) 2026 Departemen Matematika dan Sains Data FMIPA UNAND
This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.
All articles published in Jurnal Matematika UNAND (JMUA) are open access and licensed under the Creative Commons Attribution-ShareAlike (CC BY-SA) license. This ensures that the content is freely available to all users and can be shared and adapted, provided appropriate credit is given and any adaptations are distributed under the same license.
Copyright Holder
The copyright of all articles published in Jurnal Matematika UNAND is held by the Departemen Matematika dan Sains Data, Fakultas Matematika dan Ilmu Pengetahuan Alam (FMIPA), Universitas Andalas (UNAND). This applies to all published versions, including the HTML and PDF formats of the articles.
Author Rights
While the Departemen Matematika dan Sains Data FMIPA UNAND holds the copyright for all published content, authors retain important rights under the Creative Commons Attribution-ShareAlike 4.0 International License (CC BY-SA). This license grants authors and users the following rights:
- Reuse: Authors can reuse and distribute their work for any lawful purpose, including sharing on personal websites, institutional repositories, or in subsequent publications.
- Attribution and Adaptation: Authors and others may remix, adapt, and build upon the published work for any purpose, even commercially, as long as proper credit is given to the original authors, and any derivative works are distributed under the same CC BY-SA license.
Creative Commons License (CC BY-SA)
Under the terms of the CC BY-SA license, users are free to:
- Share: Copy and redistribute the material in any medium or format.
- Adapt: Remix, transform, and build upon the material for any purpose, even commercially.
However, the following conditions apply:
- Attribution: Users must give appropriate credit to the original author(s) and Departemen Matematika dan Sains Data FMIPA UNAND, provide a link to the license, and indicate if changes were made. Attribution must not imply endorsement by the author or the journal.
- ShareAlike: If users remix, transform, or build upon the material, they must distribute their contributions under the same license as the original.
For more information about the CC BY-SA license, please visit the Creative Commons website.
Third-Party Content
If authors include third-party material (such as figures, tables, or images) that is not covered by a Creative Commons license, they must obtain the necessary permissions for reuse and provide proper attribution. Authors are required to ensure that any third-party content complies with open-access licensing requirements or includes permissions for redistribution under similar terms.
Copyright and Licensing Information Display
The copyright and licensing terms will be clearly displayed on each article's landing page, as well as within the full-text versions (HTML and PDF) of all published articles.
No "All Rights Reserved"
As an open-access journal, JMUA does not use "All Rights Reserved" policies. Instead, the CC BY-SA license ensures that the works remain accessible and reusable for a wide audience while still protecting both the authors' and the copyright holder's rights.
Â
