Computing the edge metric dimension of convex polytopes related graphs

Let G = ( V ( G ) , E ( G )) be a connected graph and d ( f , y ) denotes the distance between edge f and vertex y , which is defined as d ( f , y ) = min { d ( p , y ) , d ( q , y ) } , where f = pq . A subset W E ⊆ V ( G ) is called an edge metric generator for graph G if for every two distinct edges f 1 , f 2 ∈ E ( G ) , there exists a vertex y ∈ W E such that d ( f 1 , y ) (cid:54) = d ( f 2 , y ) . An edge metric generator with minimum number of vertices is called an edge metric basis for graph G and the cardinality of an edge metric basis is called the edge metric dimension represented by edim ( G ) . In this paper, we study the edge metric dimension of flower graph f n × 3 and also calculate the edge metric dimension of the prism related graphs D (cid:48) n and D tn . It has been concluded that the edge metric dimension of D (cid:48) n is bounded, while of f n × 3 and D tn is unbounded.