Domatic And Roman Domination In Graph

This paper mainly researches into domatic and Roman domination in graph, andexplores several kinks of deformation about domatic and Roman domination, such astotal domatic, k-domatic, weak Roman domination, Roman bondage domination, andRoman domatic. The research is mainly conducted from the following aspects:Firstly, this paper discusses the boundaries of domatic and domination in graph.Based on the previous researches, this paper makes some alters to these boundaries,determines the boundaries of domatic of corona graph and product graph, andpresents the domatic number ofPm Pn.And, this paper presents the Roman domatic numbers of some special graphs(such as star graphs, circle graphs, path graphs, fan graphs, wheel graphs, andcomplete2-partite graphs, and so on).Moreover, paper extends the boundaries of Roman domatic of graphs, definesRoman bondage domination, determines some boundaries of bondage Roman domaticof graphs, and alters some present conclusions. By combining domatic with Romandomination, this paper defines Roman domatic and determines the boundaries of it.