Computing Fault-Tolerant Metric Dimension of Connected Graphs - Uzma Ahmad; Sara Ahmed; Muhammad Javaid; Md Nur Alam (Journal of Mathematics)
For a connected graph, the concept of metric dimension contributes an important role in computer networking and in the formation of chemical structures. Among the various types of the metric dimensions, the fault-tolerant metric dimension has attained much more attention by the researchers in the last decade. In this study, the mixed fault-tolerant dimension of rooted product of a graph with path graph with reference to a pendant vertex of path graph is determined. In general, the necessary and sufficient conditions for graphs of order at least 3 having mixed fault-tolerant generators are established. Moreover, the mixed fault-tolerant metric generator is determined for graphs having shortest cycle length at least 4.