STRONGLY ISOLATE DOMINATION IN GRAPHS

Abstract

This paper, we establish a newly discovered parameter called ”Strongly Isolate Domination”(SID). A dominating set ????∗ of a graph ????+ is said to be an isolate dominating set (IDS) of G if < ????∗ > has at least one isolated vertex. The ID number of ????+ is represented by ????0(????+). An ID-set ????∗ is considered as strongly isolate dominating set (SIDS) if there exists y ∈ ????∗ such that ????2(????) ∩ ????∗ = ???? , where ????2(????) = {????:????(????,????) ≤ 2 and ????≠ ????}. This paper involves some basic features of SIDS and compare SIDS with dominating set, ID-set and efficient dominating set(EDS). At the end, includes SID number of path, cycle, complete bi- partite graph, complete b- partite graph and some group of graphs.