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The k-metric dimension of a graph
As a generalization of the concept of a metric basis, this article introduces
the notion of -metric basis in graphs. Given a connected graph , a
set is said to be a -metric generator for if the elements
of any pair of different vertices of are distinguished by at least
elements of , i.e., for any two different vertices , there exist
at least vertices such that for every . A metric generator of minimum
cardinality is called a -metric basis and its cardinality the -metric
dimension of . A connected graph is -metric dimensional if is the
largest integer such that there exists a -metric basis for . We give a
necessary and sufficient condition for a graph to be -metric dimensional and
we obtain several results on the -metric dimension
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