Advances and Applications in Discrete Mathematics
Volume 7, Issue 2, Pages 145 - 151
(April 2011)
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PRINCIPAL IDEAL GRAPHS OF UNIT REGULAR MONOIDS
R. S. Indu and L. John
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with
and two vertices a and
are 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.