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 \ 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.

Automated summary

In this paper, the exact metric and fault-tolerant metric dimension of the benzenoid tripod structure are determined. The generalized version of this parameter is also computed and it is proved that all the parameters are constant. Resolving sets provide a unique representation for chemical structures and have important applications in fields such as pharmaceutical research.