PRINCIPAL IDEAL GRAPHS OF RECTANGULAR BANDS
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 GS with ( ) SGV S = and two vertices a and b ( ba ≠ ) are adjacent in GS if and only if {}≠ ∩ SbSa. The principal right ideal graph is defined accordingly and is denoted by SG. In this paper we describe the structures of principal ideal graphs of rectangular bands. We see that if ∧×IS = is a rectangular band, then GS is a disconnected graph with | | ∧ components in which each component is complete with | | I vertices, while SG is a disconnected graph with | | I components in which each component is complete with | | ∧ vertices. We also describe the number of edges in GS and SG when S is a rectangular band.