Partition Dimension of the Sum Product of Complete Graph K_1 and Saw Graph GR_n

Jusmawati Massalesse (Departemen Matematika, Universitas Hasanuddin, Makassar, Indonesia)
Dermawan Saputra (Departments of Mathematics, Hasanuddin University, Makassar - Indonesia)
Naimah Aris (Departments of Mathematics, Hasanuddin University, Makassar - Indonesia)

JURNAL MATEMATIKA STATISTIKA DAN KOMPUTASI
Vol. 21 No. 2 (2025): JANUARY 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.