Computation of Resolvability Parameters for Benzenoid Hammer Graph

Abstract

A representation of each vertex of a network into distance-based arbitrary tuple form, adding the condition of uniqueness of each vertex with reference to some settled vertices. Such settled vertices form a set known as resolving set. This idea was delivered in various problems of computer networking as well as in chemical graph theory. Due to its huge implications, many new variants were introduced such as edge resolving set, fault-tolerant version of edge, and vertex resolving set and its generalization named as partition resolving set. In this work, we addressed all these variants for a benzenoid chemical structure named a hammer graph. Moreover, we proved that all the above variants are independent of the size and order of this graph.