• 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 (vi) f (vj) where vi , vj 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.
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