Domination in Some Classes of Ditrees

Domination and other related concepts in undirected graphs are well studied. Although domination and related topics are extensively studied, the respective analogies on digraphs have not received much attention. Such studies in the directed graphs have applications in game theory and other areas. A directed graph D is a pair (V;E), where V is a non empty set and E is a set of ordered pairs of elements taken from set V . V is called vertices and E set called directed edges. Let D = (V;E) be a digraph if (x; y) 2 E then arc is directed from x to y and is denoted by x ! y. The vertex x is called a predecessor of y and y is called a successor of x. A set S  V of a digraph D is said to be a dominating set of D if 8v =2 S, v is a successor of some vertex s 2 S. In this paper we study domination theory on few well known classes of directed trees. Directed trees are extensively used in path algorithm, scheduling problems, data processing networks, data compression, causal structures like family tree, Bayesian network, moral graphs, in uence diagram etc. The concept of dominating function plays a signicant role in these models.