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Abstract
Let ψ=(V,E) be a simple connected graph. The distance between ρ1,ρ2∈V(ψ) is the length of a shortest path between ρ1 and ρ2. Let Γ={Γ1,Γ2,…,Γj} be an ordered partition of the vertices of ψ . Let ρ1∈V(ψ) , and r(ρ1|Γ)={d(ρ1,Γ1),d(ρ1,Γ2),…,d(ρ1,Γj)} be a j -tuple. If the representation r(ρ1|Γ) of every ρ1∈V(ψ) w.r.t. Γ is unique then Γ is the resolving partition set of vertices of ψ . The minimum value of j in the resolving partition set is known as partition dimension and written as pd(ψ). The problem of computing exact and constant values of partition dimension is hard so one can compute bound for the partition dimension of a general family of graph. In this paper, we studied partition dimension of the some families of convex polytopes with pendant edge such as RPn , Dpn and Qpn and proved that these graphs have bounded partition dimension.
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Additional Metadata
Item Type: | Article |
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Divisions: | Faculty of Science Institute for Mathematical Research |
DOI Number: | https://doi.org/10.3934/math.2022245 |
Publisher: | AIMS Press |
Keywords: | Resolving partition set; Bounded partition dimension; Convex polytopes |
Depositing User: | Ms. Nur Faseha Mohd Kadim |
Date Deposited: | 29 Mar 2023 08:03 |
Last Modified: | 29 Mar 2023 08:03 |
Altmetrics: | http://www.altmetric.com/details.php?domain=psasir.upm.edu.my&doi=10.3934/math.2022245 |
URI: | http://psasir.upm.edu.my/id/eprint/94422 |
Statistic Details: | View Download Statistic |
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