Sinthujah Dayaney: A Study on Domination in Graphs

Abstract: A subset \(S\subseteq V\) is a dominating set in a graph \(G = (V,E)\) if every vertex \(v \in V \setminus S\) is adjacent to at least one vertex \(v\in S\). The minimum cardinality of a dominating set is called the domination number of G and it is denoted by \(\gamma(G)\). In this thesis, we study the domination number for standard graphs and derive some upper and lower bounds for \(\gamma(G)\). The main object of this thesis is to study dominating sets.