Simultaneous Resolvability in Families of Corona Product Graphs

Let G be a graph family defined on a common vertex set V and let d be a distance defined on every graph G is an element of G . A set S subset of V is said to be a simultaneous metric generator for G if for every G is an element of G and every pair of different vertices u,v is an element of V there exists s is an element of S such that d(s,u) not equal d(s,v) . The simultaneous metric dimension of G is the smallest integer k such that there is a simultaneous metric generator for G of cardinality k. We study the simultaneous metric dimension of families composed by corona product graphs. Specifically, we focus on the case of two particular distances defined on every G is an element of G , namely the geodesic distance d(G) and the distance d(G,2) : V x V -> N boolean OR {0} defined as d(G,2)(x,y) = min{d(G)(x,y), 2}.