Endomorphisms of Cayley digraphs of~rectangular groups

Srichan Arworn ; Boyko Gyurov ; Nuttawoot Nupo ; Sayan Panma

Algebra and discrete mathematics, Tome 26 (2018) no. 2, pp. 153-169.

Résumé

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

Détail

Mots-clés : Cayley digraphs, rectangular groups, endomorphisms.

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