Partition Dimension of Complete Multipartite Graph

Authors

  • Safriadi Safriadi SMA Negeri 12 Makassar
  • Hasmawati Hasmawati Universitas Hasanuddin
  • Loeky Haryanto Universitas Hasanuddin

DOI:

https://doi.org/10.20956/jmsk.v16i3.7278

Keywords:

multipartite graph, complete multipartite, partition set, resolving partition, partition dimension

Abstract

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

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Published

2020-04-28

Issue

Vol. 16 No. 3 (2020): JMSK, MAY, 2020

Section

Research Articles

License

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

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