On Vertex-transitive Cayley Graphs of Finite Transformation Semigroups with Restricted Range
Let \(T(X)\) be the semigroup of all transformations on a set \(X\). For a non-empty subset \(Y\) of \(X\), denoted by \(T(X,Y)\) the subsemigroup of \(T(X)\) consisting of all transformations whose range is contained in \(Y\). Kelarev and Praeger in  gave necessary and sufficient conditions for all vertex-transitive Cayley graphs of semigroups. In this paper, we give similar descriptions for all vertex-transitive Cayley graphs of \(T(X,Y)\).
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