
Abstract A set S ⊆ V is said to be a simultaneous metric generator for a graph family G = { G 1 , G 2 , … , G k } , 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.
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