Total domination in lict graph

For any graph G = (V, E), lict graph [eta](G) of a graph G is the graph whose vertex set is the union of the 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. A dominating set of a graph [eta](G) , is a total lict dominating set if the dominating set does not contains any isolates. The total lict dominating number [[gamma].sub.t]([eta](G)) of the graph G is a minimum cardinality of total lict dominating set of graph G. In this paper many bounds on [[gamma].sub.t]([eta](G)) are obtained and its exact values for some standard graphs are found in terms of parameters of G. Also its relationship with other domination parameters is investigated. Key Words: Smarandachely k-dominating set, total lict domination number, lict graph, edge domination number, total edge domination number, split domination number, non-split domination number.