Partition Dimension of the Sum Product of Complete Graph K_1 and Saw Graph GR_n - Jusmawati Massalesse; Dermawan Saputra; Naimah Aris (Jurnal Matematika, Statistika dan Komputasi, 2025)
Let   and  let denote the distance between dan . The distance of  to a subset  is denote by  where  Furthermore, suppose   is an ordered partition with  for  then the representation of a vertex  with respect to  is the ordered k-tuple dinoted by . The partition  is called a distinguishing partition of  if  for every .   A distinguishing partition of  with the smallest cardinality is called the minimum distinguishing partition of , and its cardinality is called the partition dimension of . The purpose of this study is to determine the partition dimension of the join graph  and . By applying the concepts of equivalent vertices and vertices of the same level, it is shown that the partition dimension of the graph  is  where  is a natural number.