Principal Ideal Graphs of Full Transformation Semigroup

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Authors

  • Department of Mathematics, All Saints' College, Sanghumukham, Trivandrum ,IN
  • 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.