• ZONE OUT DEGREE DOMINATING EFFICIENT PARAMETERS

Abstract

A function f : V(D) {0, 1} on V(D) of a digraph D(V, A) is called Zone(zero-one) Out-degree Dominating Function (ZODF) if for any v V, N₊(v) and  f (v_i) f (v_j) where v_i , v_j N₊[v] such that f(N₊[v]) 1. A ZODF f: V {0, 1} of a digraph D(V, A) is called a lower ZODF if | f |= = 1. A ZODF f: V {0, 1} of a digraph D(V, A) is called a upper ZODF if | f | = z= n-1. A set S₊ is said to be an out-degree efficient dominating set if  N₊[v] S₊| = 1 for all v V(D), the minimum cardinality of S₊ is called out-degree efficient domination number of  D and is denoted by Z₊F D). In this paper, we introduce zone (zero-one) out-degree dominating function, efficient parameters and study them.