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 Algebra Discrete Math.: Year: Volume: Issue: Page: Find

 Algebra Discrete Math., 2018, Volume 26, Issue 2, Pages 153–169 (Mi adm678)

RESEARCH ARTICLE

Endomorphisms of Cayley digraphs of rectangular groups

Srichan Arworna, Boyko Gyurovb, Nuttawoot Nupoa, Sayan Panmac

a Department of Mathematics, Chiang Mai University, Huay Kaew Road, Chiang Mai 50200, Thailand
b School of Science and Technology, Georgia Gwinnett College, University System of Georgia
c Center of Excellence in Mathematics and Applied Mathematics, Department of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai 50200, Thailand

Abstract: Let $\operatorname{Cay}(S,A)$ denote the Cayley digraph of the semigroup $S$ with respect to the set $A$, where $A$ is any subset of $S$. The function $f\colon \operatorname{Cay}(S,A) \to \operatorname{Cay}(S,A)$ is called an endomorphism of $\operatorname{Cay}(S,A)$ if for each $(x,y) \in E(\operatorname{Cay}(S,A))$ implies $(f(x),f(y)) \in E(\operatorname{Cay}(S,A))$ as well, where $E(\operatorname{Cay}(S,A))$ is an arc set of $\operatorname{Cay}(S,A)$. We characterize the endomorphisms of Cayley digraphs of rectangular groups $G\times L\times R$, where the connection sets are in the form of $A=K\times P\times T$.

Keywords: Cayley digraphs, rectangular groups, endomorphisms.

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MSC: 05C20, 05C25, 20K30, 20M99
Revised: 09.12.2018
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Citation: Srichan Arworn, Boyko Gyurov, Nuttawoot Nupo, Sayan Panma, “Endomorphisms of Cayley digraphs of rectangular groups”, Algebra Discrete Math., 26:2 (2018), 153–169

Citation in format AMSBIB
\Bibitem{ArwGyuNup18} \by Srichan~Arworn, Boyko~Gyurov, Nuttawoot~Nupo, Sayan~Panma \paper Endomorphisms of Cayley digraphs of~rectangular groups \jour Algebra Discrete Math. \yr 2018 \vol 26 \issue 2 \pages 153--169 \mathnet{http://mi.mathnet.ru/adm678}