On the Independence Number of Cayley Digraphs of Clifford Semigroups

Abstract

Let S be a Clifford semigroup and A a subset of S. We write Cay(S,A) for the Cayley digraph of a Clifford semigroup S relative to A. The (weak, path, weak path) independence number of a graph is the maximum cardinality of an (weakly, path, weakly path) independent set of vertices in the graph. In this paper, we characterize maximal connected subdigraphs of Cay(S,A) and apply these results to determine the (weak, path, weak path) independence number of Cay(S,A).