The lict graph n(G) of a graph G is the graph whose set of vertices is the union of set of edges and the set of cut vertices of G in which two vertices are adjacent if and only if the corresponding edges are adjacent or the corresponding members of G are incident.In this paper, we initiate the study of variation of standard domination, namely weak lict domination. A weak dominating set D is a weak dominating set of n(G), if for every vertex y∈V[n(G) ]-D there is a vertex x∈D with deg⁡(x)≤deg⁡(y) and y is adjacent to x. A weak domination number of n(G) is denoted by γ_wn (G), is the smallest cardinality of a weak dominating set of n(G). We determine best possible upper and lower bounds for γ_wn (G), in terms of elements of G.

Domination Double domination restrained domination weak domination weak lict domination. Subject classification number: AMS-05C69 05C70.