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

Year 2020, , 110 - 126, 14.07.2020

Nuttawoot Nupo Chollawat Pookpıenlert

https://doi.org/10.24330/ieja.768190

Cited By: 3

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

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