Computing vertex resolvability of benzenoid tripod structure

Abstract

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 Lf of C is fault-tolerant if Lf∖b is also a resolving set, for every b in Lf. 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.

Keywords

• node-resolvability
• fault-tolerant node-resolvability
• benzenoid structure
• benzenoid tripod