Point-wise outward equitable domination

Abstract

External and internal equitability studied with the properties of either the components or the set itself. In this paper, the equitability is imposed on the individual vertices and their dominating vertices. A subset [Formula: see text] of [Formula: see text] is called a Point wise outward equitable domination if for any [Formula: see text] there exists [Formula: see text] such that [Formula: see text] and [Formula: see text] are adjacent and [Formula: see text] This concept is different from that of degree equitable domination [3,4] studied in [2] where for any vertex [Formula: see text]there exists [Formula: see text] such that [Formula: see text] This is also different from the out degree equitable domination studied in [2] where [Formula: see text] is a dominating set and for any [Formula: see text][Formula: see text] Domination with this condition is the subject matter of study of this paper.