Independence numbers and path independence numbers on Cayley digraphs of Clifford semigroups

Abstract

Consider S as a Clifford semigroup, with A being a non-empty subset of S. We use the notation Cay(S, A) to denote the Cayley digraph associated with the Clifford semigroup S in relation to A. The independence, including weak independence, path independence, and weak path independence, of a digraph is determined by the maximum cardinality of a set of vertices that are independent (or weakly independent, path independent, weakly path independent) within the digraph. In this thesis, our focus lies in characterizing the maximal connected subdigraphs of Cay(S, A) and utilizing these findings to establish both lower and upper bounds for the independence numbers. Additionally, we provide the exact values of the weak independence, path independence, and weak path independence numbers of Cay(S, A).