Partition Dimention of Amalgamation-Side in Cycle Graph
DOI:
https://doi.org/10.20956/j.v20i1.26808Keywords:
edge amalgamation, partition dimention, even order cycle graph, discrimination partition, equivalent point, graph theoryAbstract
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.
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2023 Author and publisher
This work is licensed under a Creative Commons Attribution 4.0 International 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.
