Locating and Fault-Tolerant Locating Numbers of Certain Structure.

Abstract

A branch of mathematics called chemical graph theory unifies graph theory and chemistry. Molecules are mathematically modelled using graph theory to reveal the physical characteristics of these chemical compounds. Here chemical structure can be expressed in the form of graph. In chemical graph the vertices represent the compound's atoms, and the edges represent its chemical bonds. For a connected graph ?, a resolving set is a subset of ?(?) that is used to uniquely identify all vertices of graph by means of distance codes in such a way that all the vertices have distinct codes, if the resolving set is minimum that is called basis for ? and its cardinality termed as metric dimension or location number. If all the vertices of the graph are identified by at least one pair of vertices of resolving set, then this set is referring as fault-tolerant resolving set and if this set is minimum then its cardinality is called fault-tolerant metric dimension. This thesis comprised of five main chapters whose details are: first chapter is about introduction, second consist of literature review, chapter 3 and 4 consist of main results in which we study fault-tolerant metric dimension of chemical structure. We show that this parameter is unbounded if we consider n-unit structure. Finally, in chapter 5 we present conclusion of the thesis and some future directions.