Fault-tolerant dominant metric dimension of graphs

The behavior of a graph via distance-based parameters has been widely used in various applications of daily life problems and in diverse disciplines including operation research, drug discovery, sensor networking, source localization, comparing interconnected networks, detection of network motifs, robot navigation, and image processing. Upon introducing the metric dimension as a distance-based parameter, the concept of fault-tolerant metric dimension appeared in the literature. For the dominant metric dimension of graphs introduced by the authors, a fault-tolerant parameter is needed. The purpose of this study is to introduce the concept of fault-tolerant dominant metric dimension of graphs and initiate research related to its mathematical properties. We compare fault-tolerant resolving sets with fault-tolerant dominant resolving sets. We present a method to obtain the aforesaid dimension of graphs and expressions for a family of wheel-related graphs.