Partition Dimension of Complete Multipartite Graph

Safriadi Safriadi (SMA Negeri 12 Makassar)
Hasmawati Hasmawati (Universitas Hasanuddin)
Loeky Haryanto (Universitas Hasanuddin)

JURNAL MATEMATIKA STATISTIKA DAN KOMPUTASI
Vol. 16 No. 3 (2020): JMSK, MAY, 2020

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 , .