Abstract: Let S be a semigroup.
We define the principal left ideal graph of S as the graphwithand two vertices a andare adjacent in if
and only if The
principal right ideal graph is defined accordingly and is denoted by In
this paper, we study graphs and
when
S is a unit regular monoid. We prove
that the graphs and
are
always connected. We see that the induced subgraphs and
of
and
respectively,
are always complete, where G is the
group of units in S.
Keywords and phrases: complete graph, connected graph, diameter of a graph, unit regular monoid, factorizable semigroup.
