Simultaneous Resolvability in Graph Families

A set S⊆V is said to be a simultaneous metric generator for a graph family G={G1,G2,…,Gk}, defined on a common vertex set, if it is a generator for every graph of the family. A minimum simultaneous metric generator is called a simultaneous metric basis, and its cardinality the simultaneous metric dimension of G. We study the properties of simultaneous metric generators and simultaneous metric bases, and calculate closed formulae or tight bounds for the simultaneous metric dimension of several graph families.