@article{Khali2022, 
author = {Adnan Khali and Sh. K Said Husain and Muhammad Faisal Nadeem},
title = {On bounded partition dimension of different families of convex polytopes with pendant edges},
year = {2022},
journal = {AIMS Mathematics},
volume = {7},
number = {3},
pages = {4405-4415},
keywords = {resolving partition set, bounded partition dimension, convex polytopes},
url = {https://www.sciopen.com/article/10.3934/math.2022245},
doi = {10.3934/math.2022245},
abstract = {Let    ψ  =  (  V  ,  E  ) be a simple connected graph. The distance between        ρ    1    ,      ρ    2    ∈  V  (  ψ  ) is the length of a shortest path between        ρ    1   and        ρ    2    . Let    Γ  =  {      Γ    1    ,      Γ    2    ,  …  ,      Γ    j    } be an ordered partition of the vertices of    ψ. Let        ρ    1    ∈  V  (  ψ  ), and    r  (      ρ    1        |    Γ  )  =  {  d  (      ρ    1    ,      Γ    1    )  ,  d  (      ρ    1    ,      Γ    2    )  ,  …  ,  d  (      ρ    1    ,      Γ    j    )  } be a    j-tuple. If the representation    r  (      ρ    1        |    Γ  ) of every        ρ    1    ∈  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    p  d  (  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        R    n    P  ,        D    n    p   and        Q    n    p   and proved that these graphs have bounded partition dimension.}
}