KARAKTERISASI POHON DENGAN BILANGAN DOMINASI-LOKASI-METRIK TIGA

Authors

  • Zulfaneti Zulfaneti Universitas PGRI Sumatera Barat
  • Edy Tri Baskoro Institut Teknologi Bandung
  • Hilda Assiyatun Institut Teknologi Bandung

DOI:

https://doi.org/10.25077/jmua.13.4.340-348.2024

Keywords:

Himpunan dominasi, himpunan pembeda, himpunan dominasi-lokasi- metrik

Abstract

Misalkan G = (V;E) adalah graf sederhana dan terhubung. Untuk suatu himpunan R = fr1; r2; : : : ; rkg V dan v 2 V , representasi titik v terhadap R adalah vektor r(vjR) = (d(v; r1); d(v; r2); : : : ; d(v; rk)) dimana d(v; r) menyatakan jarak titik v dan titik r. Himpunan R disebut himpunan pembeda dari G jika semua titik di G memiliki representasi unik terhadap R. Himpunan D disebut himpunan dominasi dari G jika
setiap titik di G-D bertetangga dengan suatu titik v 2 D. Suatu himpunan dominasi
dan juga merupakan himpunan pembeda disebut himpunan dominasi-lokasi-metrik dari
G. Kardinalitas dari himpunan dominasi-lokasi-metrik minimum dari G disebut bilangan dominasi-lokasi-metrik dari G. Semua graf orde n dengan bilangan dominasi-lokasi-metrik 1, 2, n-2 dan n-3 telah ditentukan secara lengkap. Dalam tulisan ini, kami
mengkarakterisasi semua pohon dengan bilangan-dominasi-lokasi-metrik 3 dan secara
khusus membuktikan bahwa tidak ada pohon dengan bilangan-dominasi-lokasi-metrik
sama dengan dimensi metriknya.

References

Brigham, R.C., Chartrand, G., Dutton, R.D. dan Zhang, P., 2003. Resolving domination in graphs. Mathematica Bohemica, Volume 128(1), pp.25-36.

Susilowati, L., Saadah, I., Fauziyyah, R. Z., Erfanian, A., 2020: The dominant metric dimension of graphs, Heliyon, 6(3), e03633.

Wangguway, Y., Wardani, D., Alfarisi, R.,2020, On resolving domination number of special family of graphs, dalam Journal of Physics: Conference Series, Vol. 1465, IOP Publishing, 012015.

Kurniawati, S., Wardani, D., Albirri, E., 2020, On resolving domination number of friendship graph and its operation, dalam Journal of Physics: Conference Series, Vol. 1465, IOP Publishing, 012019.

Adirasari, R. P., Suprajitno, H. dan Susilowati, L., 2021, The dominant metric dimension of corona product graphs, Baghdad Science Journal, 18(2), 03490349.

Henning, M.A. dan Oellermann, O.R., 2004. Metric-locating-dominating sets in graphs. Ars Combinatoria, Volume 73(129-141), p.94.

Zulfaneti, Assiyatun, H. dan Baskoro, E. T., 2022: On metric-location-domination number of graphs, International Journal of Mathematics and Computer Science, Vol:17(4), 17211733.

Gonzalez, A., Hernando, C. dan Mora, M., 2018. Metric-locating-dominating sets of graphs for constructing related subsets of vertices. Applied mathematics and computation, 332, pp.449-456.

Caceres, J. dan Pelayo, I.M., 2023. Metric Location in Pseudotrees: A survey and new results. arXiv preprint arXiv:2307.13403.

Zulfaneti. 2024. Penentuan dan Karakterisasi Bilangan Dominasi-Lokasi-Metrik Beberapa Kelas Graf. Disertasi di Institut Teknologi Bandung. Tidak diterbitkan.

Slater, P. J., 1975. Leaves of trees,Proc. 6th Southeastern Conf. on Combinatorics, Graph Theory, and Computing, Congr. Numer., 14, 549559.

Zulfaneti dan Baskoro, E.T., 2021. The Metric-Location-Domination Number of k-Paths. In Journal of Physics: Conference Series (Vol. 1722, No. 1, p. 012054). IOP Publishing.

Downloads

Additional Files

Published

31-10-2024

Issue

Vol. 13 No. 4 (2024)

Section

Articles

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