Structural properties and isomorphism theorems for Cayley digraphs of full transformation semigroups with respect to Green's equivalence classes

Nuttawoot Nupo; Yanisa Chaiya

doi:10.1016/j.heliyon.2023.e12976

Structural properties and isomorphism theorems for Cayley digraphs of full transformation semigroups with respect to Green's equivalence classes

Heliyon. 2023 Jan 13;9(1):e12976. doi: 10.1016/j.heliyon.2023.e12976. eCollection 2023 Jan.

Authors

Nuttawoot Nupo¹, Yanisa Chaiya²

Affiliations

¹ Department of Mathematics, Faculty of Science, Khon Kaen University, Khon Kaen, 40002, Thailand.
² Department of Mathematics and Statistics, Faculty of Science and Technology, Thammasat University, Pathum Thani, 12120, Thailand.

Abstract

Let $T (X)$ be the full transformation semigroup on a nonempty set X. In this paper, the Cayley digraphs of $T (X)$ with connection sets L and R, the Green's equivalence classes of $T (X)$ according to the Green's relations $L$ and $R$ , are investigated. Furthermore, their connectedness properties are characterized. In addition, the isomorphism theorems for Cayley digraphs of $T (X)$ are also presented.

Keywords: Cayley digraph; Connectedness; Full transformation semigroup; Green's relations; Isomorphism theorem.