- International Electronic Journal of Algebra
- Vol: 28 Issue: 28
- ON CONNECTEDNESS AND COMPLETENESS OF CAYLEY DIGRAPHS OF TRANSFORMATION SEMIGROUPS WITH FIXED SETS
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 : 10 | Download : 5
Publication Date : 2020-07-14
Article Type : Research
Abstract :Let $\text{Fix}(X,Y)$ 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 $\text{Fix}(X,Y)$ and study some structural properties of such digraphs such as the connectedness and the completeness. Further, some prominent results of Cayley digraphs of $\text{Fix}(X,Y)$ relative to minimal idempotents are verified. In addition, the characterization of an equivalence digraph of the Cayley digraph of $\text{Fix}(X,Y)$ is also investigated.Keywords : Cayley digraphs of transformation semigroups, connectedness, completeness, minimal idempotents, equivalence digraphs