Partition Dimension of Complete Multipartite Graph
DOI:
https://doi.org/10.20956/jmsk.v16i3.7278Keywords:
multipartite graph, complete multipartite, partition set, resolving partition, partition dimensionAbstract
Determining a resolving partition of a graph is an interesting study in graph theory due to many applications like censor design, compound classification in chemistry, robotic navigation and internet network. Let and , the distance between an is . For an ordered partition of , the representation of with respect to is . The partition is called a resolving partition of if all representation of vertices are distinct. The partition dimension of graph is the smallest integer such that has a resolving partition with element.
In this thesis, we determine the partition dimension of complete multipartite graph , which is limited by , with and . We found that , , and , .
References
Chartrand, G., Salehi, E. dan Zhang, P. 2000. The partition dimension of a graph. Aequationes Mathematicae.
Chartrand, G.,. dan Zhang, P. Salehi, E. 1998. On the partition dimension of a graph. Congressus Numerantium.
Fehr, M., Gosselin, S. Dan Oellermann, O. 2006. The partition dimension of Cayley digraphs. Aequationes Mathematicae.
Garey, M. dan Johnson, D. 1979. Computers and Intractability: A Guide to the Theory of NP-completeness, W.H. Freeman: California.
Gross, J.L. dan Yellen, J. 2004. Hand Book of Graph Theory. CRC Press LLC: Florida
Hasmawati. 2007. Bilangan Ramsey Untuk Graf Gabungan Bintang. Disertasi tidak diterbitkan. Bandung : Program Pascasarjana ITB.
Javaid, I. Dan Shokat, S. 2008. On the partition dimension of some wheel related graphs. Journal of prime Research in Mathematics.
Lipschutz dan Lipson. 2002. Matematika diskrit. Salemaba teknika: jakarta.
Melter, R. Dan Tomescu, I. 1984. Metric bases in digital geometri. Computer vision Graphics and image Processing.
Tomescu, I. 2008. Discrepancies between metric dimension and partition dimension of a connected graph, Discrete Mathematics.
Tomescu, I., Javaid, I. dan Slamin. 2007. On the partition dimension and connected partition dimension of wheels. Ars Combinatoria.
Downloads
Published
Issue
Section
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.
