#### The Partition Dimension of a Path Graph

##### Abstract

Resolving partition is part of graph theory. This article, explains about resolving partition of the path graph, with. Given a connected graph  and  is a subset of  writen . Suppose there is , then the distance between and  is denoted in the form . There is an ordered set of -partitions of, writen then  the representation of with respect tois the  The set of partitions ofis called a resolving partition if the representation of each  to  is different. The minimum cardinality of the solving-partition to  is called the partition dimension of G which is denoted by . Before getting the partition dimension of a path graph, the first step is to look for resolving partition of the graph. Some resolving partitions of path graph,  with ,  and  are obtained. Then, the partition dimension of the path graph which is the minimum cardinality of resolving partition, namely pd (Pn)=2Resolving partition is part of graph theory. This article, explains about resolving partition of the path graph, with. Given a connected graph  and  is a subset of  writen . Suppose there is , then the distance between and  is denoted in the form . There is an ordered set of -partitions of, writen then  the representation of with respect tois the  The set of partitions ofis called a resolving partition if the representation of each  to  is different. The minimum cardinality of the solving-partition to  is called the partition dimension of G which is denoted by . Before getting the partition dimension of a path graph, the first step is to look for resolving partition of the graph. Some resolving partitionsof path graph, with ,  and  are obtained. Then, the partition dimension of the path graph which is the minimum cardinality of resolving partition, namely.