Bilangan Kromatik Lokasi Pada Graf Lobster L_(n,m,1) untuk 6≤m≤16 dan n=2,3,4

Authors

  • Tika Apriliza Universitas Andalas
  • DES WELYYANTI
  • LYRA YULIANTI

DOI:

https://doi.org/10.25077/jmua.11.2.95-103.2022

Keywords:

Bilangan Kromatik Lokasi, Graf Lobster, Kode Warna,

Abstract

Misalkan G = (V, E)  graf terhubung dan c suatu k-pewarnaan dari G. Kelas warna pada G adalah himpunan titik-titik yang berwarna i, dinotasikan dengan S_(i) untuk  1≤i≤k. Misalkan Π adalah suatu partisi terurut dari V(G) kedalam kelas-kelas warna yang saling bebas S_1,S_2, ...,S_k, dengan titik-titik di S_i diberi warna i, 1≤i≤k. Jarak suatu titik v ke S_i dinotasikan dengan (v,C_i) adalah min {d(v,x)|x  S_i}. Kode warna dari suatu titik v V didefinisikan  sebagai k-vektor yaitu:

              (v)=(d(v,S_(1)), d(v,S_(2)), ...,d(v,S_(k)))

dimana d(v,S_(i)) = min {d(v,x)|x  S_i}.  untuk 1≤i≤k .  Jika setiap titik yang berbeda di G memiliki kode warna yang berbeda untuk suatu Π maka  disebut pewarnaan lokasi untuk G. Jumlah warna minimum yang digunakan pada pewarnaan lokasi dari graf G disebut bilangan kromatik lokasi untuk G, dinotasikan dengan (G). Pada tulisan ini akan dibahas bilangan kromatik lokasi graf lobster L_(n,m,1) untuk 6≤m≤16 dan n=2,3,4.

 

 

References

{1} Asmiati. 2013. Graf Lobster Berbilangan Kromatik Lokasi Empat. Prosiding Semirata FMIPA Universitas Lampung.

{2} Chartrand, G., M.A. Henning, P.J. Slater, dan P. Zhang. 2002. The locating-chromatic number of a graph. {Bull.Inst. Combin. Appl}.{36}:89-101.

{3} Chartrand, G., Zhang,P. 2005.{ Introduction to Graph Teory}. McGraw-Hill, New York.

{4} Chartrand, G., Zhang,P. 2009. { Chromatic Graph Theory }. Chapman

and Hall/CRC.

{5}Silvia, M., Welyyanti, D., Efendi , . 2018. {Bilangan Kromatik Lokasi Pada Graf Lobster L_{n,m,1} dengan n=2,3,4 dan m=3. Jurnal Matematika Universitas Andalas. Vol.VII No.3 Hal 94-103.

Downloads

Additional Files

Published

30-04-2022

Issue

Vol. 11 No. 2 (2022)

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