Partition Dimension of the Sum Product of Complete Graph K_1 and Saw Graph GR_n

Authors

  • Jusmawati Massalesse Departemen Matematika, Universitas Hasanuddin, Makassar, Indonesia
  • Dermawan Departments of Mathematics, Hasanuddin University, Makassar - Indonesia
  • Naimah Departments of Mathematics, Hasanuddin University, Makassar - Indonesia

DOI:

https://doi.org/10.20956/j.v21i2.32376

Keywords:

partition dimension, sum product of graph, complete graph, saw graph, equivalent vertices, level vertices

Abstract

Let   and  let denote the distance between dan . The distance of  to a subset  is denote by  where  Furthermore, suppose   is an ordered partition with  for  then the representation of a vertex  with respect to  is the ordered k-tuple dinoted by . The partition  is called a distinguishing partition of  if  for every .   A distinguishing partition of  with the smallest cardinality is called the minimum distinguishing partition of , and its cardinality is called the partition dimension of . The purpose of this study is to determine the partition dimension of the join graph  and . By applying the concepts of equivalent vertices and vertices of the same level, it is shown that the partition dimension of the graph  is  where  is a natural number.

References

[1] Auliya, N., 2014. Dimensi Partisi pada Graf K_1+ mCn, m, n∈ N, n≥ 3. Skripsi. Malang: Universitas Islam Negeri Maulana Malik Ibrahim.

[2] Chartrand, G., Salehi, E. & Zhang, P., 2002. The Partition Dimension of a Graph. Aequationes Mathematicae, 59, 45 – 54.

[3] Darmaji, 2011. Dimensi Partisi Graf Multipartit dan Graf Hasil Korona Dua Graf Terhubung. Disertasi. Bandung: Institut Teknologi Bandung.

[4] Faisal, F., Mardiana, N. & Rosiyanti, H., 2019. Dimensi Partisi Graf Hasil Operasi Comb Graf Lingkaran dan Graf Lintasan. Jurnal Pendidikan Matematika dan Matematika, Vol 5, No. 2, 163-174.

[5] Hamidi, M. R., 2022. Penentuan Dimensi Partisi Pada Graf Hasil Korona Antara Graf Lengkap dengan Graf Roda. Skripsi. Makassar: Universitas Hasanuddin.

[6] Hasmawati, 2020. Bahan Ajar Teori Graf. Makassar: UPT Unhas Press.

[7] Hasmawati, Nurwahyu, B., Daming, A.S. & Amir, A.K., 2021. Partition Dimention of Dutch Windmill Graph. Jurnal Matematika, Statistika dan Komputasi, Vol. 17 No.3, 472–483.

[8] Mauliddiyah, R., 2023. Dimensi Metrik Graf Hasil Operasi Korona Graf Gergaji GR_n Dengan Graf Lengkap K_1. Skripsi. Makassar: Universitas Hasanuddin.

[9] Munir, R., 2003. Matematika Diskrit, Edisi kedua. Bandung: Informatika.

[10] Purwaningsih, S., 2017. Dimensi Partisi Graf Lintasan Korona Graf Bintang P_m K_1, n untuk m ≥ 1 dan n≥ 3. Jurnal Matematika UNAND, 6(2), 16-19.

[11] Ramdhani, V., 2019. Dimensi Partisi Graf Lengkap. Sainstek: Jurnal Sains dan Teknologi, Vol. 11, No. 2, 65-69.

Downloads

Published

2025-01-12

How to Cite

Massalesse, J., Saputra, D., & Aris, N. (2025). Partition Dimension of the Sum Product of Complete Graph K_1 and Saw Graph GR_n. Jurnal Matematika, Statistika Dan Komputasi, 21(2), 573–582. https://doi.org/10.20956/j.v21i2.32376

Issue

Vol. 21 No. 2 (2025): JANUARY 2025

Section

Research Articles

License

Copyright (c) 2025 Jurnal Matematika, Statistika dan Komputasi

Creative Commons License

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

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

Jurnal Matematika, Statistika dan Komputasi is an Open Access journal, all articles are distributed under the terms of the Creative Commons Attribution License, allowing third parties to copy and redistribute the material in any medium or format, transform, and build upon the material, provided the original work is properly cited and states its license.  This license allows authors and readers to use all articles, data sets, graphics and appendices in data mining applications, search engines, web sites, blogs and other platforms by providing appropriate reference.

Most read articles by the same author(s)

<< < 1 2 3