The Locating Chromatic Number of Pizza Graphs Containing a Single Path on the Outer Vertices

Authors

  • Agus Irawan Institut Teknologi Sumatera
  • Nasrullah Bachtiar Institut Teknologi Sumatera
  • Miftahul Irfan Institut Teknologi Sumatera
  • Aldila Nur Indah Berliana Ratam Institut Teknologi Sumatera
  • M. Marisa Institut Teknologi Sumatera
  • Nanda Azzanina Institut Teknologi Sumatera

DOI:

https://doi.org/10.24252/msa.v13i2.60573

Keywords:

locating chromatic number, Pizza graphs, single path

Abstract

In graph theory, the locating chromatic number refers to the minimum number of colours required to colour the vertices of a graph such that each vertex is uniquely identifiable by its own colour and the colours of its neighbouring vertices. This concept is associated with graph coloring, which entails assigning colors to a graph's vertices in such a way that no two adjacent vertices have the same color. It determines the minimum number of colours necessary to produce a proper vertex colouring. This research focuses on determining the locating chromatic number of Pizza graphs containing a single path on the outer vertices.

References

G. Chartrand, E. Salehi, and P. Zhang, “The partition dimension of a graph,” Aequationes Math., vol. 59, no. 1–2, pp. 45–54, 2000, doi: 10.1007/PL00000127.

V. Saenpholphat and P. Zhang, “Conditional resolvability in graphs: A survey,” Int. J. Math. Math. Sci., vol. 2004, no. 38, pp. 1997–2017, 2004, doi: 10.1155/S0161171204311403.

G. Chartrand, D. Erwin, M. A. Henning, P. J. Slater, and P. Zhang, “The locating-chromatic number of a graph,” Bull. Inst. Comb. it’s Appl., vol. 36, pp. 89–101, 2002.

A. Irawan, A. Asmiati, L. Zakaria, and K. Muludi, “The locating-chromatic number of origami graphs,” Algorithms, vol. 14, no. 6, pp. 1–15, 2021, doi: 10.3390/a14060167.

A. Irawan, Asmiati, S. Suharsono, and K. Muludi, “The locating-chromatic number of certain barbell origami graphs,” J. Phys. Conf. Ser., vol. 1751, no. 1, pp. 1–12, 2021, doi: 10.1088/1742-6596/1751/1/012017.

A. Irawan, Asmiati, L. Zakaria, K. Muludi, and U. Bernadhita, H, S, “Subdivision of Certain Barbell Operation of Origami Graphs has Locating-Chromatic Number Five,” vol. 21, no. 9, 2021.

A. Irawan, B. H. S. Utami, A. Nuryaman, and K. Muludi, “A Procedure for Determining The Locating Chromatic Number of An Origami Graphs,” IJCSNS Int. J. Comput. Sci. Netw. Secur., vol. 22, no. 9, pp. 2–5, 2022, [Online]. Available: https://doi.org/10.22937/IJCSNS.2022.22.9.5.

Asmiati, A. Irawan, A. Nuryaman, and K. Muludi, “The locating chromatic number for certain operation of origami graphs,” Math. Stat., vol. 11, no. 1, pp. 101–106, 2023, doi: 10.13189/ms.2023.110111.

W. D. A. Nur Hamzaha, Asmiatia, “Locating Chromatic Number for Corona Operation of Path Pn and Cycle Cm(m = 3,4),” Indones. J. Comb., vol. 8, no. 2, pp. 127–135, 2024, doi: 10.7546/nntdm.2019.25.2.190-198.

I. W. Sudarsana, F. Susanto, and S. Musdalifah, “The locating chromatic number for m-shadow of a connected graph,” Electron. J. Graph Theory Appl., vol. 10, no. 2, pp. 589–601, 2022, doi: 10.5614/ejgta.2022.10.2.18.

S. Nabila and A. N. M. Salman, “The rainbow connection number of origami graphs and pizza graphs,” Procedia Comput. Sci., vol. 74, no. December, pp. 162–167, 2015, doi: 10.1016/j.procs.2015.12.093.

N. M. Surbakti, D. Kartika, H. Nasution, and S. Dewi, “The Locating Chromatic Number for Pizza Graphs,” Sainmatika J. Ilm. Mat. dan Ilmu Pengetah. Alam, vol. 20, no. 2, pp. 126–131, 2023, doi: 10.31851/sainmatika.v20i2.13085.

Downloads

Published

2025-12-18

How to Cite

[1]
A. Irawan, N. Bachtiar, M. Irfan, A. N. I. B. Ratam, M. Marisa, and N. Azzanina, “The Locating Chromatic Number of Pizza Graphs Containing a Single Path on the Outer Vertices”, MSA, vol. 13, no. 2, pp. 184–189, Dec. 2025.

Issue

Vol. 13 No. 2 (2025): VOLUME 13 NO 2, 2025

Section

Artikel

License

Copyright (c) 2025 Jurnal MSA ( Matematika dan Statistika serta Aplikasinya)

Creative Commons License

This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.

Copyright Notice

Jurnal MSA (Matematika dan Statistika serta Aplikasinya)

Authors who publish in Jurnal MSA agree to the following copyright and licensing terms.

1. Copyright Ownership

Authors retain copyright in their scholarly articles unless copyright is lawfully held by another authorized rights holder.

Publication in Jurnal MSA does not require an exclusive transfer or assignment of copyright ownership to the journal or its publisher.

2. Non-Exclusive Publishing Rights

Authors or authorized copyright holders grant Jurnal MSA non-exclusive rights of first journal publication, dissemination, indexing, and digital preservation.

These rights allow the journal to publish, reproduce, distribute, archive, and preserve the accepted scholarly article without transferring copyright ownership.

3. Publication License

Jurnal MSA adopts and applies the Creative Commons Attribution 4.0 International License (CC BY 4.0) as the standard license for scholarly articles published under its current publication terms.

Authors or authorized rights holders authorize publication of their articles under CC BY 4.0.

This license permits sharing, reproduction, redistribution, adaptation, and reuse, including commercial reuse, subject to the license terms and attribution requirements.

Official License:

https://creativecommons.org/licenses/by/4.0/

4. Non-Commercial Publishing Model

Jurnal MSA operates as a non-commercial scholarly publisher dedicated to education, scientific research, and scholarly communication.

The journal's non-commercial status does not restrict commercial reuse of articles licensed under CC BY 4.0.

5. Authors' Rights and Self-Archiving

Authors retain their applicable rights to reuse, share, and disseminate their scholarly works.

Authors may immediately deposit and distribute the published version of their CC BY 4.0-licensed articles through institutional repositories, disciplinary repositories, and academic websites without an embargo imposed by the journal.

Such distribution remains subject to the applicable license and third-party rights.

6. Author Consent and Third-Party Rights

By agreeing to publication, the corresponding author confirms that:

  1. All listed authors have approved the manuscript and the publication arrangements.

  2. The authors or authorized rights holders possess the legal authority necessary to authorize publication and licensing.

  3. Jurnal MSA is granted the necessary non-exclusive publishing rights.

  4. Publication of the article under CC BY 4.0 is authorized.

  5. Required permissions for third-party materials have been obtained, and any licensing exclusions have been clearly identified.

7. Previously Published Articles

Articles published before the implementation of the current licensing policy remain governed by their validly applicable copyright and licensing arrangements.

The adoption of CC BY 4.0 does not automatically change licenses previously granted under different terms.

Copyright and License Statement

Copyright © [Year], The Author(s).

The author(s) retain copyright and grant Jurnal MSA non-exclusive rights of first publication, dissemination, indexing, and preservation.

This article is licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0).

https://creativecommons.org/licenses/by/4.0/

Most read articles by the same author(s)