Studies in domination and related topics

Abstract

This thesis embodies the work done by the author under the guidance newlineof Dr.S.Petchimuthu. The idea of domination in graphs was introduced by Ore. newlineFor the period of last thirty years domination has fast growth of research in its newlinearea. newlineIn this Thesis, we investigate the properties of different types of newlinedomination parameters. newline1. Intersection Empty Domination Number newline2. Perfect Edge Domination Number newline3. Connected Perfect Edge Domination Number newline4. Common Edge Domination Number newline5. Intersection Empty Edge Domination Number newline6. Isolate Bondage Number newline7. Cototal Bondage Number newline8. Intersection Empty Bondage Number newlineAll our graphs are simple and undirected. Throughout our thesis, p and q denote newlinethe order and the size of the graph respectively. newlineIn Chapter 1, we derive the origin of graph theory and origin of newlinedomination and mention an application of domination. Moreover, we give the newlineliterature survey and we give the basic definitions. newline