Partition Dimension of the Sum Product of Complete Graph K_1 and Saw Graph GR_n - Jusmawati Massalesse; Dermawan Saputra; Naimah Aris (Department of Mathematics, Hasanuddin University, 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.