Edge Metric Dimension of Some Graph Operations

Let G = ( V , E ) be a connected graph. Given a vertex v ∈ V and an edge e = u w ∈ E , the distance between v and e is defined as d G ( e , v ) = min { d G ( u , v ) , d G ( w , v ) } . A nonempty set S ⊂ V is an edge metric generator for G if for any two edges e 1 , e 2 ∈ E there is a vertex w ∈ S such that d G ( w , e 1 ) ≠ d G ( w , e 2 ) . The minimum cardinality of any edge metric generator for a graph G is the edge metric dimension of G . The edge metric dimension of the join, lexicographic, and corona product of graphs is studied in this article.