# The Partition Dimension on the Grid Graph

## Authors

• Haspika Haspika Universitas hasanuddin
• Hasmawati Hasmawati
• Naimah Aris

## Keywords:

grid graph, partition dimensions, resolving partition, partition set

## Abstract

Graph G is a discrete set pair with the notation V(G)   with its element called a vertex and the set of different and unordered pairs with the notation E(G)   where the element is called edge. One type of graph Gm,n is a grid graph that is notated  is a graph of the result of the operation between two path graphs (Pm*Pn).  The set of partition∏ ={S1,S2,…,Sk} of V(G) is called a resolving partition if its representation for each vertex on graph G is different. The cardinality of the minimum resolving partition of graph G is the partition dimension of the graph G denoted pd(G). This paper discusses the dimension of the grid graph partition Gm,n  with the result pd(Gm,n) = 3 for m,n>=2 with n even value.

## References

Chartrand, G., Salehi, E., & Zhang, P., 2000. The Partition Dimension of a Graph. Aequationes Math. No. 59, 45-54.

Darmaji, 2011. Dimensi Partisi Graf Multipartit dan Graf Hasil Korona Dua Graf Terhubung. Disertasi. Jurusan Matematika FMIPA ITB. Bandung.

Dwi Dayanti, D., 2018. Infimum Passing Grade Prodi Pendidikan Matematika UNSIKA 2017. Sesiomadika, 187-195.

Grigorious, C., Stephen, S., Rajan, B., Miller, M. & William, A., 2014. On the partition dimension of a class of circulant graphs. Information Processing Letters, Vol. 114, No. 7, 353-356.

Hasmawati, 2020. Pengantar dan Jenis-Jenis Graf. UPT Unhas Press, Makassar.

Hasmawati, Nurwahyu, B., Syukur Daming, A., & Kamal Amir, A., 2021. Dimensi Partisi Graf Kincir Angin Belanda. Jurnal Matematika, Statistika dan Komputasi, Vol. 17, No. 3, 472-483.

Hernando, C., Mora, M., Pelayo, I. M., Seara, C., cceres, J., & Puertas, M. L., 2005. On the metric dimension of some families of graphs. Eletronic Notes in Discrete mathematics. No. 22, 129-133.

Ida Bagus Kade Puja Arimbawa, K., & Baskoro, E.T., 2015. Partition Dimension of Some Classes of Trees, Procedia Computer Science, 74, 67-72.

Khuller, S., dan Raghavachari, B., 1996. Landmark in Graph. Discrete Appl. Math. No.70, 217-229.

Mehreen, N., Farooq, R., & Akhter. S., 2018. On partition dimension of fullerene graphs,AIMS Mathematics, Vol. 3, No. 3, 343-352.

Moreno, E., 2020. On the k-partition Dimension of graphs. Theoretical computer science, 806, 42-52.

Permana, A., B,. & Darmaji, 2012. Dimensi Metrik Graf Pohon Bentuk Tertentu, Jurnal Teknik Pomits, Vol. 1, No. 1, 1- 4.

Sudha, S., & Manikanda, K., 2015. General Pattern of Total Coloring of a Prims Graph of n-Layers and a Grid Graph. Internasional Journal of Innovative Science and Modern Engineering, Vol. 3, No. 03.

Ur Rehman, T., & Mehreen,. N., 2020. Partition Dimension and Strong Metric Dimension of Chain Cycle, Jordan Journal of mathematics and statistics,Vol. 13, No. 2, 305-325.

Wijaya, K., 2010. Struktur Aljabar Ring. UPT Penerbitan Universitas Jember. Jember.

2023-01-05

## How to Cite

Haspika, H., Hasmawati, H., & Aris, N. . (2023). The Partition Dimension on the Grid Graph. Jurnal Matematika, Statistika Dan Komputasi, 19(2), 351-358. https://doi.org/10.20956/j.v19i2.23904

## Section

Research Articles

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