Abstract
A graph has a vertex set and edge set and . A non - empty subset D is an independent dominating set if every vertex in is adjacent a vertex in and is a non – adjacent vertices. The domination number is the minimum cardinality of an independent dominating set. If, in addition let and be the element of . Then weakly dominates if (i) and (ii) . A set S is a weak non-split dominating set of if every vertex is is weakly dominated by at least one vertex in and the induced subgraph is connected. The minimum cardinality of a weak non-split independent dominating set is the weak non-split independent domination number of G .The main purpose of this paper is to introduce the concept of weak non-split independent domination number. For that we have chosen Soifer graph, Chvatal graph, Fritsch graph, Herschel graph, Moser graph, Franklin graph to find the weak non-split domination number.
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