On the Partition Dimension of Honey Comb, Hexagonal Cage Networks and Quartz Network

Abstract

Let v and P be a vertex and subset V(G) of a simple connected graph G and the distance between v and P is defined by . Let  be a K resolving vertex partition of G then a distinct vertex representation of a vertex v with respect to  is . The partition dimension of G is the minimum cardinality of the resolving partition set and it is denoted by  In this paper we have determined partition dimension of Honeycomb Cage Network of dimension n with two-layer, Hexagonal Cage Network and Quartz Network.