Minimum Fault-Tolerant, local and strong metric dimension of graphs

Abstract: In this paper, we consider three similar optimization problems: the fault-tolerant metric dimension problem, the local metric dimension problem and the strong metric dimension problem. These problems have applications in many diverse areas, including network discovery and verification, robot navigation and chemistry, etc. We give integer linear programming formulations of the fault-tolerant metric dimension problem and the local metric dimension problem. Also, we study local metric dimension and strong metric dimension of two convex polytopes $S_n$ and $U_n$.