@article{Koam2024, 
author = {Ali N. A. Koam and Adnan Khalil and Ali Ahmad and Muhammad Azeem},
title = {Cardinality bounds on subsets in the partition resolving set for complex convex polytope-like graph},
year = {2024},
journal = {AIMS Mathematics},
volume = {9},
number = {4},
pages = {10078-10094},
keywords = {convex polytope-like graph, bounded partition dimension, partition dimension, partition resolving set},
url = {https://www.sciopen.com/article/10.3934/math.2024493},
doi = {10.3934/math.2024493},
abstract = {Let    G  =  (  V  ,  E  ) be a simple, connected graph with vertex set    V  (  G  ) and    E  (  G  ) edge set of    G. For two vertices    a and    b in a graph    G, the distance    d  (  a  ,  b  ) from    a to    b is the length of shortest path    a  −  b path in    G. A    k-ordered partition of vertices of    G is represented as        R        p    =  {      R              p      1        ,      R              p      2        ,  …  ,      R              p      k        } and the representation    r  (  a      |        R        p    ) of a vertex    a with respect to        R        p   is the vector    (  d  (  a      |        R              p      1        )  ,  d  (  a      |        R              p      2        )  ,  …  ,  d  (  a      |        R              p      k        )  ). The partition is called a resolving partition of    G if    r  (  a      |        R        p    )  ≠  r  (  b      |        R        p    ) for all distinct    a  ,  b  ∈  V  (  G  ). The partition dimension of a graph, denoted by    p  d  (  G  ), is the cardinality of a minimum resolving partition of    G. Computing precise and constant values for the partition dimension poses a interesting problem; therefore, it is possible to compute an upper bound for the partition dimension within a general family of graphs. In this paper, we studied partition dimension of the some families of convex polytopes, specifically              T        n  ,              U        n  ,              V        n  , and              A        n  , and proved that these graphs have constant partition dimension.}
}