AIMS Mathematics, 2020, 5(6): 5541-5550. doi: 10.3934/math.2020355.

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On topological spaces generated by simple undirected graphs

Department of Mathematics, Faculty of Science, University of Atatürk, Erzurum, 25240, Turkey

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.
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Keywords graph theory; topological space; homeomorphism; equivalence of the graphs

Citation: Hatice Kübra Sarı, Abdullah Kopuzlu. On topological spaces generated by simple undirected graphs. AIMS Mathematics, 2020, 5(6): 5541-5550. doi: 10.3934/math.2020355


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