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

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<abstract><p>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 $ \Gamma = \{\Gamma_1, \Gamma_2, \dots, \Gamma_j\} $ be an ordered partition of the vertices of $ \psi $. Let $ \rho_1\in V(\psi) $, and $ r(\rho_1|\Gamma) = \{d(\rho_1, \Gamma_1), d(\rho_1, \Gamma_2), \dots, d(\rho_1, \Gamma_j)\} $ be a $ j $-tuple. If the representation $ r(\rho_1|\Gamma) $ of every $ \rho_1\in V(\psi) $ w.r.t. $ \Gamma $ is unique then $ \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.</p></abstract>