Strongly Isolate Perfect Domination in Graphs

A dominating set of a graph is said to be an isolate dominating set (IDS) if < > has at least one isolated vertex. The ID number of is represented by . An ID-set is considered as strongly isolate dominating set (SIDS) if there exists a ∈ such that , where and . A dominating set is called a perfect dominating set if every vertex in V (G) − has exactly one neighbour in . By using the above concept and the definition of SID, we define a new concept called ”Strongly Isolate Perfect Domination”(SIPD). An isolate dominating set is said to be strongly isolate perfect dominating set if there exists such that and is a perfect dominating set of . This paper involves some basic features of SIPDS and compare SIPDS with dominating set, ID-set and efficient dominating set (EDS). At the end, includes SIPD number of path, cycle, complete bi- partite graph, complete b- partite graph and some group of graphs.