Study on Split and Independent Strong Domination Parameters of Some Families of Graphs

Abstract

The study of domination has emerged as a significant area of research not only in newlinegraph theory but also in combinatorial optimization and analysis of algorithms as well. newlineGraph domination is the assignment of the vertex subset of a graph subject to certain newlineconstraints. The dominating set is a subset D of the vertex set V such that every newlinevertex in V and#8722; D is adjacent to a vertex in D, with the constraint that |D| is minimum. newlineAdditional constraints on the set D, the set V and#8722;D, or the method by which the set V and#8722;D newlineis defined, variants of the domination parameters such as connected domination number, newlineindependent domination number, and total domination numbers can be acquired. newlineThis thesis focuses mainly on two types of domination, namely Split domination newlinenumber, and Independent strong domination number. Also, the relation between these newlinetwo domination parameters and locating split domination number in graphs are explored newlinein this study newline