On connected cayley graphs of semigroups

Abstract

© 2015 by the Mathematical Association of Thailand. All rights reserved. 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 to the case of semigroups and give some necessary and sufficient conditions for Cayley graphs of a semigroup to be connected. We also characterize weakly connected Cayley graphs of a semigroup and indicate a relationship between a Cayley graph of a semigroup and the Hasse diagram of a partially ordered set.