Study On Some Types Of Domination Parameters Of Graphs

There are six chapters in this thesis.The first chapter is overview, in which we introduce the developing status aboutDomination Parameter and some related work that we have done.In the second chapter, we show that the maximum number of edges that a connectedbipartite graph with n vertices, domination numberγ≥3 and the maximum degreeIn the third chapter, we discuss whether some particular classes of graphs are independentdomination bicritical and study the properties of independent domination bicritical graphs,then ways of constructing an independent domination bicritical graph from smallerindependent domination bicritical graphs are presented.In the fourth chapter, we characterize trees with equal 2-component domination anddomination numbers. That is, the necessary and sufficient conditions forγ_c~2(T)=γ(T) andγ_c~2(T)=γ_c(T) are given.In the fifth chapter, we characterize trees and unicyclic graphs with equal connecteddomination and 2-component domination numbers. That is, if G is a tree or a unicyclic graph,the necessary and sufficient conditions forγ_c (G)=γ_c~2 (G) are given.In the sixth chapter, we study some properties of k-component restrained dominationnumber and the necessary and sufficient conditions for restrained domination number equalsk-component restrained domination number (k=1,2) are given if G is a tree or a unicyclicgraph.