On Connectedness of Cayley Graphs of Finite Transformation Semigroups

Chunya Tisklang, Sayan Panma

Abstract

For a fixed non-empty subset Y of X, we denote by T(X, Y ) the
semigroup consisting of all transformations on X whose range is contained in Y . In
this paper, we investigate connectedness of Cayley graphs of finite transformation
semigroups with restricted range. Necessary and sufficient conditions for Cayley
graph of T(X, Y ) to be strongly connected, unilaterally connected, and weakly
connected are given.