On Sharp Bounds on Partition Dimension of Convex Polytopes

LetΩbe a connected graph and for a givenl-ordered partition of vertices of a connected graphΩis represented asβ =\β ₁,β ₂, ,β ₗ\. The representation of a vertexμ ∈ V(Ω)is the vectorr(μ |β)=(d(μ,β ₁),d(μ,β ₂), , d(μ,β ₗ)). The partitionβis a resolving partition for vertices ofΩif all vertices ofΩhaving the unique representation with respect toβ. The minimum number oflin the resolving partition forΩis known as the partition dimension ofΩand represented aspd(Ω). Resolving partition and partition dimension have multipurpose applications in networking, optimization, computer, mastermind games and modeling of chemical structures. The problem of computing constant values of partition dimension is NP-hard so one can find sharp bound for the partition dimension of graph. In this article, we computed the upper bound for the convex polytopesEₙ,~Sₙ,~Tₙ,~Gₙ,~Qₙand flower graphfn× 3.