ON CONNECTEDNESS AND COMPLETENESS OF CAYLEY DIGRAPHS OF TRANSFORMATION SEMIGROUPS WITH FIXED SETS

Authors : Nuttawoot NUPO, Chollawat POOKPIENLERT

Pages : 110-126

Doi:10.24330/ieja.768190

View : 17 | Download : 10

Publication Date : 2020-07-14

Article Type : Research Paper

Abstract :Let $\text{Fix}insert ignore into journalissuearticles values(X,Y);$ 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 $\text{Fix}insert ignore into journalissuearticles values(X,Y);$ and study some structural properties of such digraphs such as the connectedness and the completeness. Further, some prominent results of Cayley digraphs of $\text{Fix}insert ignore into journalissuearticles values(X,Y);$ relative to minimal idempotents are verified. In addition, the characterization of an equivalence digraph of the Cayley digraph of $\text{Fix}insert ignore into journalissuearticles values(X,Y);$ is also investigated.
Keywords : Cayley digraphs of transformation semigroups, connectedness, completeness, minimal idempotents, equivalence digraphs