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Graph homomorphisms of partial monounary algebras. (English) Zbl 1108.08002
A partial monounary algebra is a pair $$(V,f)$$, where $$V$$ is a nonempty set and $$f$$ is a partial unary operation defined on $$A\subseteq V$$. Partial monounary algebras can be represented by graphs. To each partial monounary algebra $$(V,f)$$ there correspond two graphs, $$G(V,f)=(V,E)$$ and $$G'(V,f)=(V,E')$$ such that $$E$$ and $$E'$$ are binary operations on $$V$$ defined by putting $$(x,y)\in E$$ if and only if $$f(x)=y$$, and $$(x,y)\in E'$$ if and only if $$x\neq y$$ and $$f(x)=y$$. Therefore the graph $$G(V,f)$$ admits loops while $$G'(V,f)$$ contains no loops. By means of the strong homomorphism of graphs the notions of a $$G$$-homomorphism and a $$G'$$-homomorphism of partial monounary algebras are introduced and studied in this paper.

##### MSC:
 08A55 Partial algebras 08A60 Unary algebras
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