Principal Ideal Graphs of Full Transformation Semigroup Jump To References Section Authors R. S. Indu Department of Mathematics, All Saints' College, Sanghumukham, Trivandrum ,IN L. John Department of Mathematics, University of Kerala, Trivandrum ,IN Keywords: Complete Graph, Induced Subgraph, Null Graph, Principal Ideal Graphs, Full Transformation Semigroup. Abstract 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.