Partition Dimention of Amalgamation-Side in Cycle Graph

Authors

  • Ananda Dwi Nabila Nanda Dept. mathematics, Hasanuddin University
  • Hasmawati Hasmawati Dept. of Mathematics, Hasanuddin University
  • Muh. Nur Dept. of Mathematics, Hasanuddin University

DOI:

https://doi.org/10.20956/j.v20i1.26808

Keywords:

edge amalgamation, partition dimention, even order cycle graph, discrimination partition, equivalent point, graph theory

Abstract

The graph  is a pair of sets , where  is a finite set whose elements are called vertices, and  is the set of pairs of members of .  which is called the edge. Let  be a simple graph where . The distance between points  and  is denoted by  is the length of the shortest path between  and . Given  and there is a vertex  on the connected graph , then the distance between  and  is denoted . If  is -partition of , then the representation of  with respect to is -ordered pairs, . If the -ordered pairs  for   are all different, then the partition is called a dimension partition. The minimal -number which is the -differentiating partition of  is called the partition dimension of  and is denoted by . In this study, the partition dimensions of the sided amalgamation result will be determined on an even-order cycle graph. In determining the dimensions of the partition, characterization of the partition dimensions is used in the path graph, the lemma about the distinguishing set and the equivalence point, especially in the even-order cycle graph. The results of this study are pd(Amal(Cn,e,k)) = 3 for n≥4 ,  pd(Amal(C4,e,k))=4 for k=4 , pd(Amal(C4,e,k))=3+m for  k=2m+3 and k=2m+4  where m=1,2,3,...

References

Chartrand, G., Salehi, E., & Zhang, P., 2000. The Partition Dimension of a Graph. Aequationes Mathematica, 59, 45-54.

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

Hasmawati., 2015. Bahan Ajar Teori Graf. Universitas Hasanuddin, Makassar.

Hasmawati., Hinding, N., Nurwahyu, B., Daming, A. S., & Amir, A. K., 2022. The Partition Dimension of The Vertex Amalgamation of Some Cycles. Heliyon, Vol. 8, Issue 6.

Indriyani, RA. N., 2013. Dimensi Metrik dan Dimensi Partisi pada Graf Amalgamasi Sisi Siklus Gasal. Universitas Airlangga, Surabaya.

Liza, G. A., 2018. Dimensi Partisi dari Graf Persahabatan. Jurnal Matematika UNAND, Vol. 7, No. 3, 54-58.

Monica, Mohan. C., Santhakumar, S., 2019. Partition Dimension of Rooted Product Graphs.

Elseiver, Vol. 262, No. 12, 138-147.

Wei, C., Nadeem, M. F., Siddiqui, H. M. A., Azeem, M., Liu, J., & Khalil, A., 2021. On

Partition Dimension of Some Cycle-Related Graphs. Hindawi, Vol. 2021, No. 4, 1-8.

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Published

2023-09-06

Issue

Vol. 20 No. 1 (2023): SEPTEMBER, 2023

Section

Research Articles

License

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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.

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