Appears in collection : Metric dimension in graphs and related topics

A resolving set in a graph G is a set of vertices of G with the property that all the vertices of the graph are uniquely identified by the resolving set, by means of a vector of distances to such set. The metric dimension of the graph G is then the cardinality of a smallest possible resolving set of G. The resolving sets and the metric dimension of graphs have several applications in diverse practical problems arising in computer science, chemistry and social sciences, among other ones. This course of four lectures is focused on the presentation of several results concerning the metric dimension of graphs, and some of its variants. The results that will be discussed shall cover different properties of this graph parameter. There will be emphasis on their combinatorial properties, but there will be also much information on computational and applied issues of the metric dimension of graphs and some of its variants.