Endomorphisms of Cayley digraphs of rectangular groups

Abstract

Let Cay(S, A) denote the Cayley digraph of the semigroup S with respect to the set A, where A is any subset of S. The function f : Cay(S, A) → Cay(S, A) is called an endo-morphism of Cay(S, A) if for each (x, y) ∈ E(Cay(S, A)) implies (f(x), f(y)) ∈ E(Cay(S, A)) as well, where E(Cay(S, A)) is an arc set of Cay(S, A). We characterize the endomorphisms of Cayley digraphs of rectangular groups G × L × R, where the connection sets are in the form of A = K × P × T.