LAUSR

Let $$G=(V, E)$$ G = ( V , E ) be a connected graph. Given a vertex $$v\in V$$ v ∈ V and an edge $$e=uw\in E$$ e = u w ∈ E , the distance between v and e is defined as $$d_G(e,v)=\min \{d_G(u,v),d_G(w,v)\}$$ d G ( e , v ) = min { d G ( u , v ) , d G ( w , v ) } . A nonempty set $$S\subset V$$ S ⊂ V is an edge metric generator for G if for any two edges $$e_1,e_2\in E$$ e 1 , e 2 ∈ E there is a vertex $$w\in S$$ w ∈ S such that $$d_G(w,e_1)\ne d_G(w,e_2)$$ 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.