ABSTRACT
AswesaidintheProlegomenon,thisisabookaboutdominatingsetsingraphs. Havingdefinedgraphsandmanyfundamentaltermsingraphtheory,weare nowinapositiontodefineanddiscusstheconceptofadominatingsetina graph.Throughaseriesofapplications,wewillalsopresentseveraldifferent typesofdominatingsets.Wewillconsiderthedifficultyofdesigningalgorithms forfindingdominatingsetsofminimumcardinalityinagraph,whichleadsto adiscussionofcomputationalcomplexityandNP-completeness.Weconclude thischapterwithabriefreviewofthehistoricaldevelopmentofthestudyof dominationingraphs.
