Abstract
Every node in a network is said to be resolved if it can be uniquely identified by a vector of distances to a specific set of nodes. The metric dimension is equivalent to the least possible cardinal number of a resolving set. Conditional resolving sets are obtained by imposing various constraints on resolving set. It is a fundamental parameter that provides insights into the structural properties and navigability of graphs, with diverse applications across different fields. This article focuses on identifying the metric dimension for a new network, star fan graph.