Resolving sets tolerant to failures in three-dimensional grids

Abstract An ordered set S of vertices a graph G is resolving for if every vertex uniquely determined by its vector distances to the in . The metric dimension minimum cardinality set. In this paper we study sets tolerant several failures three-dimensional grids. Concretely, seek that are after removing any k from This equivalent finding $$(k+1)$$ ( k + 1 ) - , generalization sets, where, pair vertices, differs at least $$k+1$$ coordinates. problem also related with graph, defined as -resolving work, first prove grid 3 and establish some properties involving these graphs. Secondly, determine values $$k\ge 1$$ ≥ which there exists construct such almost all cases.