Computing Fault‐Tolerant Metric Dimension of Connected Graphs

Abstract

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.

Locating-dominating number of certain infinite families of convex polytopes with applications

“…Specifically, [5] and [6] revealed that the metric dimension of , , , , and are equal to 3, while [7] explored minimizing doubly-resolving sets and strong resolvability of and . In addition, Salman et al [8] analyzed three optimization problems including the strong metric, fault-tolerant as well as the local metric dimension problems and applied them to and families of convex polytopes. Next, due to Simić et al [9] , we present an updated integer linear programming model for the locating-dominating number of graphs.…”