On topological spaces generated by simple undirected graphs
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. Finall...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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AIMS Press
2020-07-01
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| Series: | AIMS Mathematics |
| Subjects: | |
| Online Access: | https://www.aimspress.com/article/10.3934/math.2020355/fulltext.html |
| _version_ | 1828827843421798400 |
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| author | Hatice Kübra Sarı Abdullah Kopuzlu |
| author_facet | Hatice Kübra Sarı Abdullah Kopuzlu |
| author_sort | Hatice Kübra Sarı |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-12-12T15:09:34Z |
| format | Article |
| id | doaj.art-8cfc1e244d9e494e8c683dfaffe8ced7 |
| institution | Directory Open Access Journal |
| issn | 2473-6988 |
| language | English |
| last_indexed | 2024-12-12T15:09:34Z |
| publishDate | 2020-07-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj.art-8cfc1e244d9e494e8c683dfaffe8ced72022-12-22T00:20:40ZengAIMS PressAIMS Mathematics2473-69882020-07-01565541555010.3934/math.2020355On topological spaces generated by simple undirected graphsHatice Kübra Sarı0Abdullah Kopuzlu1Department of Mathematics, Faculty of Science, University of Atatürk, Erzurum, 25240, TurkeyDepartment of Mathematics, Faculty of Science, University of Atatürk, Erzurum, 25240, TurkeyIn 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.https://www.aimspress.com/article/10.3934/math.2020355/fulltext.htmlgraph theorytopological spacehomeomorphismequivalence of the graphs |
| spellingShingle | Hatice Kübra Sarı Abdullah Kopuzlu On topological spaces generated by simple undirected graphs AIMS Mathematics graph theory topological space homeomorphism equivalence of the graphs |
| title | On topological spaces generated by simple undirected graphs |
| title_full | On topological spaces generated by simple undirected graphs |
| title_fullStr | On topological spaces generated by simple undirected graphs |
| title_full_unstemmed | On topological spaces generated by simple undirected graphs |
| title_short | On topological spaces generated by simple undirected graphs |
| title_sort | on topological spaces generated by simple undirected graphs |
| topic | graph theory topological space homeomorphism equivalence of the graphs |
| url | https://www.aimspress.com/article/10.3934/math.2020355/fulltext.html |
| work_keys_str_mv | AT haticekubrasarı ontopologicalspacesgeneratedbysimpleundirectedgraphs AT abdullahkopuzlu ontopologicalspacesgeneratedbysimpleundirectedgraphs |