Title of article :
ON CONNECTEDNESS and COMPLETENESS OF CAYLEY DIGRAPHS OF TRANSFORMATION SEMIGROUPS WITH FIXED SETS
Author/Authors :
Nupo, Nuttawoot Department of Mathematics - Faculty of Science - Khon Kaen University, Thailand , Pookpienlert, Chollawat Department of Mathematics - Faculty of Science and Agricultural Technology - Rajamangala University of Technology Lanna, Thailand
Abstract :
Let Fix(X, Y ) be a semigroup of full transformations on a set X
in which elements in a nonempty subset Y of X are fixed. In this paper, we
construct the Cayley digraphs of Fix(X, Y ) and study some structural properties of such digraphs such as the connectedness and the completeness. Further,
some prominent results of Cayley digraphs of Fix(X, Y ) relative to minimal
idempotents are verified. In addition, the characterization of an equivalence
digraph of the Cayley digraph of Fix(X, Y ) is also investigated
Keywords :
Cayley digraphs of transformation semigroups , connectedness , completeness , minimal idempotents , equivalence digraphs
Journal title :
International Electronic Journal of Algebra
