Connectedness of endo-cayley digraphs of right(left) zero union of semigroups

Abstract

Let S be a finite semigroup, A a subset of S and f an endomor- phism on S. The endo-Cayley digraph of S corresponding to a connecting set A and an endomorphism f, denoted by endo - Cay f (S,A) is a digraph whose vertex set is S and a vertex u is adjacent to vertex v if and only if v = f(u)a for some a ∈ A. In this paper, we study about the connected properties of endo-Cayley di-graphs of cartesian product between semigroups and right(left) zero semigroups. We show the type of connected that they can be. Moreover, we also generalize endo-Cayley digraphs of that product into tensor product resulting graphs. © 2012 Academic Publications, Ltd.