• ZONE IN 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) In-degree Dominating Function (ZIDF) 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 ZIDF f: V {0, 1} of a digraph D(V, A) is called a lower ZIDF if  | f | = = 1. A ZIDF f : V {0, 1} of a digraph D(V, A) is called a upper ZIDF if  | f | = = n-1. A set S_- is said to be an in-degree efficient dominating set if | N_-[v] S_-| = 1 for all v V(D), the minimum cardinality of S_- is called in-degree efficient domination number of  D and is denoted by Z_-F D). In this paper, we introduce zone (zero-one) in-degree dominating function, efficient parameters and study them.