Partition Dimension of Generalized Petersen Graph

Let G=VG,EG be the connected graph. For any vertex i∈VG and a subset B⊆VG, the distance between i and B is di;B=mindi,j|j∈B. The ordered k-partition of VG is Π=B1,B2,…,Bk. The representation of vertex i with respect to Π is the k-vector, that is, ri|Π=di,B1,di,B2,…,di,Bk. The partition Π is called t...

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Autores principales:	Hassan Raza, Jia-Bao Liu, Muhammad Azeem, Muhammad Faisal Nadeem
Formato:	article
Lenguaje:	EN
Publicado:	Hindawi-Wiley 2021
Materias:	Electronic computers. Computer science QA75.5-76.95
Acceso en línea:	https://doaj.org/article/2f8d74fe273943829127d7d522168d02
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spelling	oai:doaj.org-article:2f8d74fe273943829127d7d522168d022021-11-08T02:37:13ZPartition Dimension of Generalized Petersen Graph1099-052610.1155/2021/5592476https://doaj.org/article/2f8d74fe273943829127d7d522168d022021-01-01T00:00:00Zhttp://dx.doi.org/10.1155/2021/5592476https://doaj.org/toc/1099-0526Let G=VG,EG be the connected graph. For any vertex i∈VG and a subset B⊆VG, the distance between i and B is di;B=mindi,j\|j∈B. The ordered k-partition of VG is Π=B1,B2,…,Bk. The representation of vertex i with respect to Π is the k-vector, that is, ri\|Π=di,B1,di,B2,…,di,Bk. The partition Π is called the resolving (distinguishing) partition if ri\|Π≠rj\|Π, for all distinct i,j∈VG. The minimum cardinality of the resolving partition is called the partition dimension, denoted as pdG. In this paper, we consider the upper bound for the partition dimension of the generalized Petersen graph in terms of the cardinalities of its partite sets.Hassan RazaJia-Bao LiuMuhammad AzeemMuhammad Faisal NadeemHindawi-WileyarticleElectronic computers. Computer scienceQA75.5-76.95ENComplexity, Vol 2021 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Electronic computers. Computer science QA75.5-76.95
spellingShingle	Electronic computers. Computer science QA75.5-76.95 Hassan Raza Jia-Bao Liu Muhammad Azeem Muhammad Faisal Nadeem Partition Dimension of Generalized Petersen Graph
description	Let G=VG,EG be the connected graph. For any vertex i∈VG and a subset B⊆VG, the distance between i and B is di;B=mindi,j\|j∈B. The ordered k-partition of VG is Π=B1,B2,…,Bk. The representation of vertex i with respect to Π is the k-vector, that is, ri\|Π=di,B1,di,B2,…,di,Bk. The partition Π is called the resolving (distinguishing) partition if ri\|Π≠rj\|Π, for all distinct i,j∈VG. The minimum cardinality of the resolving partition is called the partition dimension, denoted as pdG. In this paper, we consider the upper bound for the partition dimension of the generalized Petersen graph in terms of the cardinalities of its partite sets.
format	article
author	Hassan Raza Jia-Bao Liu Muhammad Azeem Muhammad Faisal Nadeem
author_facet	Hassan Raza Jia-Bao Liu Muhammad Azeem Muhammad Faisal Nadeem
author_sort	Hassan Raza
title	Partition Dimension of Generalized Petersen Graph
title_short	Partition Dimension of Generalized Petersen Graph
title_full	Partition Dimension of Generalized Petersen Graph
title_fullStr	Partition Dimension of Generalized Petersen Graph
title_full_unstemmed	Partition Dimension of Generalized Petersen Graph
title_sort	partition dimension of generalized petersen graph
publisher	Hindawi-Wiley
publishDate	2021
url	https://doaj.org/article/2f8d74fe273943829127d7d522168d02
work_keys_str_mv	AT hassanraza partitiondimensionofgeneralizedpetersengraph AT jiabaoliu partitiondimensionofgeneralizedpetersengraph AT muhammadazeem partitiondimensionofgeneralizedpetersengraph AT muhammadfaisalnadeem partitiondimensionofgeneralizedpetersengraph
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Partition Dimension of Generalized Petersen Graph

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