On Partition Dimension of Some Cycle-Related Graphs

On Partition Dimension of Some Cycle-Related Graphs

Let G be a simple connected graph. Suppose Δ=Δ1,Δ2,…,Δl an l-partition of VG. A partition representation of a vertex α w.r.t Δ is the l−vector dα,Δ1,dα,Δ2,…,dα,Δl, denoted by rα|Δ. Any partition Δ is referred as resolving partition if ∀αi≠αj∈VG such that rαi|Δ≠rαj|Δ. The smallest integer l is referr...

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Main Authors: Changcheng Wei, Muhammad Faisal Nadeem, Hafiz Muhammad Afzal Siddiqui, Muhammad Azeem, Jia-Bao Liu, Adnan Khalil
Format: Article
Language:English
Published: Hindawi Limited 2021-01-01
Series:Mathematical Problems in Engineering
Online Access:http://dx.doi.org/10.1155/2021/4046909
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spelling doaj-f0a73c7a74544007ab36492e770c60772021-03-22T00:04:31ZengHindawi LimitedMathematical Problems in Engineering1563-51472021-01-01202110.1155/2021/4046909On Partition Dimension of Some Cycle-Related GraphsChangcheng Wei0Muhammad Faisal Nadeem1Hafiz Muhammad Afzal Siddiqui2Muhammad Azeem3Jia-Bao Liu4Adnan Khalil5Department of Mathematics and Computer ScienceDepartment of MathematicsDepartment of MathematicsDepartment of MathematicsSchool of Mathematics and PhysicsDepartment of MathematicsLet G be a simple connected graph. Suppose Δ=Δ1,Δ2,…,Δl an l-partition of VG. A partition representation of a vertex α w.r.t Δ is the l−vector dα,Δ1,dα,Δ2,…,dα,Δl, denoted by rα|Δ. Any partition Δ is referred as resolving partition if ∀αi≠αj∈VG such that rαi|Δ≠rαj|Δ. The smallest integer l is referred as the partition dimension pdG of G if the l-partition Δ is a resolving partition. In this article, we discuss the partition dimension of kayak paddle graph, cycle graph with chord, and a graph generated by chain of cycles. It has been shown that the partition dimension of the said families of graphs is constant.http://dx.doi.org/10.1155/2021/4046909
collection DOAJ
language English
format Article
sources DOAJ
author Changcheng Wei
Muhammad Faisal Nadeem
Hafiz Muhammad Afzal Siddiqui
Muhammad Azeem
Jia-Bao Liu
Adnan Khalil
spellingShingle Changcheng Wei
Muhammad Faisal Nadeem
Hafiz Muhammad Afzal Siddiqui
Muhammad Azeem
Jia-Bao Liu
Adnan Khalil
On Partition Dimension of Some Cycle-Related Graphs
Mathematical Problems in Engineering
author_facet Changcheng Wei
Muhammad Faisal Nadeem
Hafiz Muhammad Afzal Siddiqui
Muhammad Azeem
Jia-Bao Liu
Adnan Khalil
author_sort Changcheng Wei
title On Partition Dimension of Some Cycle-Related Graphs
title_short On Partition Dimension of Some Cycle-Related Graphs
title_full On Partition Dimension of Some Cycle-Related Graphs
title_fullStr On Partition Dimension of Some Cycle-Related Graphs
title_full_unstemmed On Partition Dimension of Some Cycle-Related Graphs
title_sort on partition dimension of some cycle-related graphs
publisher Hindawi Limited
series Mathematical Problems in Engineering
issn 1563-5147
publishDate 2021-01-01
description Let G be a simple connected graph. Suppose Δ=Δ1,Δ2,…,Δl an l-partition of VG. A partition representation of a vertex α w.r.t Δ is the l−vector dα,Δ1,dα,Δ2,…,dα,Δl, denoted by rα|Δ. Any partition Δ is referred as resolving partition if ∀αi≠αj∈VG such that rαi|Δ≠rαj|Δ. The smallest integer l is referred as the partition dimension pdG of G if the l-partition Δ is a resolving partition. In this article, we discuss the partition dimension of kayak paddle graph, cycle graph with chord, and a graph generated by chain of cycles. It has been shown that the partition dimension of the said families of graphs is constant.
url http://dx.doi.org/10.1155/2021/4046909
work_keys_str_mv AT changchengwei onpartitiondimensionofsomecyclerelatedgraphs
AT muhammadfaisalnadeem onpartitiondimensionofsomecyclerelatedgraphs
AT hafizmuhammadafzalsiddiqui onpartitiondimensionofsomecyclerelatedgraphs
AT muhammadazeem onpartitiondimensionofsomecyclerelatedgraphs
AT jiabaoliu onpartitiondimensionofsomecyclerelatedgraphs
AT adnankhalil onpartitiondimensionofsomecyclerelatedgraphs
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