Partition Dimension of the Sum Product of Complete Graph K_1 and Saw Graph GR_n
DOI:
https://doi.org/10.20956/j.v21i2.32376Keywords:
partition dimension, sum product of graph, complete graph, saw graph, equivalent vertices, level verticesAbstract
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.
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