The Partition Dimension of a Path Graph
DOI:
https://doi.org/10.31958/js.v13i2.4719Keywords:
The Partition Dimension, Path Graph, Resolving Partition.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, withReferences
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Chartrand, G., & Lesniak, L. (1979). Graph and Digraph. Second edition. A division of Wadsworf. Inc.
Chartrand, G., & Oellermann, O. R. (1993). Applied And Algorithmic Graph Theory. United States Copyright Act.
Chartrand, G., Raines, M., & Zhang, P. (2000). The Directed Distance Dimension of Oriented Graphs.Mathematica Bohemica (2nd ed.).
Chartrand, G., Salehi, E., & Zhang, P. (2000). The Partition Dimension of a Graph. Aequationes Math (2nd ed.).
Goodaire, E. G., & Parmenter, M. M. (2002). Discrete Mathematics with Graph Theory. Prentice Hall.
Javaid, I., & Shokat, S. (2008). The partition dimension of some wheel related graphs. J. Prime Res. Math., 4(January 2008), 154–164.
Parment, M. M., & Goodaire, E. G. (2002). Discrete Mathematis with Graph Theory. Prentice-Hall, Inc.
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2021-12-31
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