We study the relationship between the graph inverse semigroups of two graphs when there is a directed immersion between the graphs and we provide structural information about graph inverse semigroups of finite graphs that admit a directed cover onto a bouquet of circles. We provide a topological characterization of the universal groups of the local submonoids of a graph inverse semigroup. We also find necessary and sufficient conditions for a homomorphic image of a graph inverse semigroup to be another graph inverse semigroup.

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关于图逆半群

当两个图之间存在有向浸入时，我们研究了两个图的图逆半群之间的关系，并且我们提供了关于有限图的图逆半群的结构信息，这些有限图允许有向覆盖到一束圆上。我们提供了图逆半群的局部子群的通用群的拓扑特征。我们还找到了一个图逆半群的同态图像是另一个图逆半群的充要条件。