On bounded partition dimension of different families of convex polytopes with pendant edges

Let $\psi =(V,E)$ be a simple connected graph. The distance between ${\rho }_1,{\rho }_2\in V(\psi )$ is the length of a shortest path between ${\rho }_1$ and ${\rho }_2.$ Let $\mathrm{\Gamma }=\{{\mathrm{\Gamma }}_1,{\mathrm{\Gamma }}_2,\dots ,{\mathrm{\Gamma }}_j\}$ be an ordered partition of the vertices of $\psi$. Let ${\rho }_1\in V(\psi )$, and $r({\rho }_1|\mathrm{\Gamma })=\{d({\rho }_1,{\mathrm{\Gamma }}_1),d({\rho }_1,{\mathrm{\Gamma }}_2),\dots ,d({\rho }_1,{\mathrm{\Gamma }}_j)\}$ be a $j$-tuple. If the representation $r({\rho }_1|\mathrm{\Gamma })$ of every ${\rho }_1\in V(\psi )$ w.r.t. $\mathrm{\Gamma }$ is unique then $\mathrm{\Gamma }$ is the resolving partition set of vertices of $\psi$. The minimum value of $j$ in the resolving partition set is known as partition dimension and written as $pd(\psi ).$ 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.