Semicomplete absorbent sets in digraphs

Abstract

Let be a digraph and S a subset of vertices of D, S is an absorbent set if for every v in there exists a vertex u in S such that A subset S of V(D) is a semicomplete absorbent set if S is absorbent and the induced subdigraph is semicomplete. The minimum (respectively maximum) of the cardinalities of the semicomplete absorbent sets is the lower (respectively upper) semicomplete absorbent number, denoted by (respectively ). In this paper we introduce the concept of semicomplete absorbent set; we will show some structural properties on the digraphs which have a semicomplete absorbent set and we will present some bounds for and Then we will study the Cartesian product, the composition of digraphs and the line digraph in relation with those numbers.