On Connectedness of Cayley Graphs of Finite Transformation Semigroups: Chunya Tisklang, Sayan Panma - Team, Support (Thai Journal of Mathematics, 2023)
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.