Resumen de Distance-equalizer sets of graphs
A. González, C. Hernando, M. Mora
A subset S of vertices of a connected graph G is a distance-equalizer set if for every twodistinct vertices x, y ∈ V (G) \ S there is a vertex w ∈ S such that the distances from xand y to w are the same. The equidistant dimension of G is the minimum cardinality of adistance-equalizer set of G. This paper studies these sets and explores its properties andapplications to other mathematical problems. Concretely, we first establish some boundsconcerning the order, the maximum degree, the clique number and the independence number,and characterize all graphs attaining some extremal values. We then study distance-equalizersets in several families of graphs. Finally, we show the usefulness of distance-equalizer setsfor constructing doubly resolving sets.
