In this paper, we study topologies generated by simple undirected graphs without isolated vertices and their properties. We generate firstly a topology using a simple undirected graph without isolated vertices. Moreover, we investigate properties of the topologies generated by certain graphs. Finally,we present continuity and opennes of functions defined from one graph to another via the topologies generated by the graphs. From this point of view, we present necessary and sufficient condition for the topological spaces generated by two different graphs to be homeomorphic.

中文翻译：

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关于简单无向图生成的拓扑空间

在本文中，我们研究了由没有隔离顶点的简单无向图生成的拓扑及其属性。首先，我们使用一个没有孤立顶点的简单无向图来生成拓扑。此外，我们研究某些图生成的拓扑的属性。最后，我们介绍了通过图生成的拓扑从一个图定义到另一个图的功能的连续性和开放性。从这一观点出发，我们提出了由两个不同图生成的拓扑空间为同胚的充要条件。