Work

Green's graphs of a semigroup

Year: 2025

Type: article

Abstract: Let S S be a semigroup. In this study, we first introduce the Green’s digraphs and Green’s graphs related to the Green’s relations L {\mathscr{L}} , R {\mathscr{R}} , and J {\mathscr{J}} of S S . Further, the connectedness and completeness of the Green’s graphs are discussed. For a finite semigroup S S , we show that each of the Green’s graphs of S S has a transitive orientation. Moreover, we obtain that these Green’s graphs are perfect. Finally, the structures of the Green’s graphs are characterized using the generalized lexicographic product.

Source: Open Mathematics

DOI: 10.1515/math-2025-0187

Authors: Yanliang Cheng, Yong Shao, Xuanlong Ma

Institutions: Hunan University of Science and Technology, Northwest University, Xi'an Shiyou University

Language: English

Topic: semigroups and automata theory

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $1,187

Funder: National Natural Science Foundation of China