Geodesic
Endomorphisms of Cayley digraphs of~rectangular groups
Algebra and discrete mathematics, Tome 26 (2018) no. 2, pp. 153-169.

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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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Srichan Arworn; Boyko Gyurov; Nuttawoot Nupo; Sayan Panma. Endomorphisms of Cayley digraphs of~rectangular groups. Algebra and discrete mathematics, Tome 26 (2018) no. 2, pp. 153-169. http://geodesic.mathdoc.fr/item/ADM_2018_26_2_a0/

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