Computing vertex resolvability of benzenoid tripod structure

In this paper, we determine the exact metric and fault-tolerant metric dimension of the benzenoid tripod structure. We also computed the generalized version of this parameter and proved that all the parameters are constant. Resolving set $L$ is an ordered subset of nodes of a graph $C$, in which each vertex of $C$ is distinctively determined by its distance vector to the nodes in $L$. The cardinality of a minimum resolving set is called the metric dimension of $C$. A resolving set $L_f$ of $C$ is fault-tolerant if $L_f\setminus b$ is also a resolving set, for every $b$ in $L_f.$ Resolving set allows to obtain a unique representation for chemical structures. In particular, they were used in pharmaceutical research for discovering patterns common to a variety of drugs. The above definitions are based on the hypothesis of chemical graph theory and it is a customary depiction of chemical compounds in form of graph structures, where the node and edge represents the atom and bond types, respectively.