COMPUTING THE INDEPENDENT DOMINATION METRIC DIMENSION PROBLEM OF SPECIFIC GRAPHS

We consider, in this paper, the NP-hard problem of finding the minimum independent domination metric dimension of graphs. A vertex set B of a connected graph G(V, V) resolves G if every vertex of G is uniquely identified by its vector of distances to the vertices in B. A resolving set B of G is independent if no two vertices in B are adjacent. A resolving set is dominating if every vertex of G that does not belong to B is a neighbor to some vertices in B. The cardinality of the smallest resolving set of G, the cardinality of the minimal independent resolving set, and the cardinality of the minimal independent domination resolving set are the metric dimension of G, independent metric dimension of G, and the independent domination metric dimension of G, respectively.