On Connected Cayley Graphs of Semigroups

T. Suksumran, S. Panma

Abstract

It is well known that for a finite group $G$ with a nonempty subset $A$, the Cayley graph of $G$ with respect to $A$ is connected if and only if $A$ is a
generating set of $G$. In this paper we generalize this result by
formulating some necessary and sufficient conditions for Cayley
graphs of semigroups to be connected. Applying Green's relations
taken relative to the subsemigroup $\langle A\rangle$ generated by
the set $A$, we characterize weakly connected Cayley graphs of
semigroups. A relationship between a Cayley graph of a semigroup and
the Hasse diagram of a