Edge metric dimension of some graph operations

الأصل · EN

Let G=(V, E) be a connected graph. Given a vertex v∈ V and an edge e=uw∈ E, the distance between v and e is defined as dG(e,v)={dG(u,v),dG(w,v)}. A nonempty set S⊂ V is an edge metric generator for G if for any two edges e₁,e₂∈ E there is a vertex w∈ S such that dG(w,e₁)≠ dG(w,e₂). 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.