Principal Ideal Graphs of Rees Matrix Semigroups
R. S. Indu, L. John · 2012
Let S be a finite regular 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. The principal ideal graph of Rees matrix semigroup is studied in this paper. First, we describe the necessary and sufficient condition for which two elements in a Rees matrix semigroup are adjacent in SG and GS. Then we characterise the principal ideal graphs of a Rees matrix semigroup. Finally we describe the number of edges in SG and GS and then the number of elements in E(SG)∩E(GS) when S is a Rees matrix semigroup.