### The Partition Dimension of a Path Graph

#### Abstract

*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.

#### Keywords

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PDF#### References

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DOI: http://dx.doi.org/10.31958/js.v13i2.4719

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