Vertex and edge metric dimensions of cacti

In a graph G, vertex (resp. an edge) metric generator is set of vertices S such that any pair edges) from G distinguished by at least one S. The cardinality smallest the dimension G. Sedlar and Škrekovski (0000) we determined unicyclic graphs it takes its value two consecutive integers. Therein, several cycle configurations were introduced greater values only if these present in graph. this paper extend result to cactus i.e. which all cycles are pairwise edge disjoint. We do so defining subgraph for every applying already approach involves configurations. obtained results enable us prove rank conjecture cacti. They also yield simple upper bound on dimensions conclude conjecturing same holds general.