COMPUTING THE INDEPENDENT DOMINATION METRIC DIMENSION PROBLEM OF SPECIFIC GRAPHS
Basma Mohamed, Iqbal M. Batiha, Mohammad Odeh, Mohammed El‐Meligy · JOURNAL OF MECHANICS OF CONTINUA AND MATHEMATICAL SCIENCES · 2024
We consider, in this paper, the NP-hard problem of finding the minimum independent domination metric dimension of graphs. A vertex set of a connected graph resolves if every vertex of is uniquely identified by its vector of distances to the vertices in . A resolving set of is independent if no two vertices in are adjacent. A resolving set is dominating if every vertex of that does not belong to is a neighbor to some vertices in . The cardinality of the smallest resolving set of , the cardinality of the minimal independent resolving set, and the cardinality of the minimal independent domination resolving set are the metric dimension of , independent metric dimension of , and the independent domination metric dimension of , respectively.