Studies in graph Theory domination related Parameters in graphs

Abstract

By a graph G V E we mean a finite undirected graph newlinewithout loops or multiple edges For basic definitions and graph newlinetheoretic terminologies we refer to Chartrand Lesniak 2005 newlineand Harary 1972 newlineIn Chapter 1 we collect some basic definitions and theorems newlineon graphs which are needed for the subsequent chapters newlineIn Chapter 2 we investigate the independence saturation newlinenumber of some classes of graphs Acharya 1980 initiated a study newlineof domsaturation The least positive integer k such that every vertex newlineof G lies in a dominating set of cardinality k is called the domsaturation newlinenumber of G and is denoted by ds G Arumugam Kala newline 2002 2004 2009 obtained further results on domsaturation Subramanian newline 2004 introduced the concept of independence saturation newlineNumber newline newline