On Sharp Bounds on Partition Dimension of Convex Polytopes

Let Omega be a connected graph and for a given l -ordered partition of vertices of a connected graph Omega is represented as beta = {beta(1), beta(2), ... , beta(l)}. The representation of a vertex mu is an element of V (Omega) is the vector r (mu vertical bar beta) = (d (mu, beta(1)), d (mu, beta(2)), ... , d (mu, beta(l))): The partition beta is a resolving partition for vertices of Omega if all vertices of Omega having the unique representation with respect to beta. The minimum number of l in the resolving partition for Omega is known as the partition dimension of Omega and represented as pd (Omega): 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 polytopes E-n; S-n; T-n; G(n); Q(n) and flower graph f(nx3).