Based on the previously obtained concrete characterization of the endomorphism semigroups of quasi-acyclic reflexive graphs we prove the relatively elementary definability of the class of such graphs in the class of all semigroups. It will permit us to investigate for such graphs the abstract representation problem for the endomorphism semigroups of graphs and the problem of elementary definability of graphs by their endomorphism semigroups.

中文翻译：

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关于半群类中图类的相对基本可定义性

基于先前获得的拟无环自反图自同半群的具体刻画，我们证明了此类图类在所有半群类中的相对基本的可定义性。它将允许我们研究此类图的自同态半群的抽象表示问题和图的自同态半群的基本可定义性问题。