Principal Ideal Graphs of Full Transformation Semigroup

Let S be a semigroup. We define the principal left ideal graph of S as the graph _SG with V (_SG)=S and two vertices a and b (a≠b) are adjacent in _SG if and only if Sa∩Sb≠ {}. The principal right ideal graph is defined accordingly and is denoted by GS. In this paper we study graphs _SG and GS when S is a Full Transformation Semigroup. We give a necessary and sufficient condition for two elements α and β in S to have an edge between them in _SG. We also describe the degree of an element in _SG, when S=ℑ(X). Finally we see that the principal right ideal graph of ℑ(X) is always complete.