Z-graphic topology on undirected graph
In this work, we define $\mathcal{Z}_{G}$ a topology on the vertex set of a graph $G$ which preserves the connectivity of the graph, called $\mathcal{Z}$-graphic topology. We prove that two isomorphic graphs have homeomorphic and symmetric $\mathcal{Z}$-graphic topologies. We show that $\mathcal{Z}...
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| Format: | Article |
| Language: | English |
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Elsevier
2023-03-01
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| Series: | Kuwait Journal of Science |
| Online Access: | https://journalskuwait.org/kjs/index.php/KJS/article/view/17541 |
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| _version_ | 1849727754538319872 |
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| author | Hanan Omer Zomam Makkia Dammak |
| author_facet | Hanan Omer Zomam Makkia Dammak |
| author_sort | Hanan Omer Zomam |
| collection | DOAJ |
| description |
In this work, we define $\mathcal{Z}_{G}$ a topology on the vertex set of a graph $G$ which preserves the connectivity of the graph, called $\mathcal{Z}$-graphic topology. We prove that two isomorphic graphs have homeomorphic and symmetric $\mathcal{Z}$-graphic topologies. We show that $\mathcal{Z}_{G}$ is an Alexandroff topology and we give a necessary and sufficient condition for a topology to be $\mathcal{Z}$-graphic.
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| format | Article |
| id | doaj-art-8658fa3121b64401b842c255d53d488c |
| institution | DOAJ |
| issn | 2307-4108 2307-4116 |
| language | English |
| publishDate | 2023-03-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Kuwait Journal of Science |
| spelling | doaj-art-8658fa3121b64401b842c255d53d488c2025-08-20T03:09:45ZengElsevierKuwait Journal of Science2307-41082307-41162023-03-01502A10.48129/kjs.17541Z-graphic topology on undirected graphHanan Omer Zomam0Makkia Dammak1Dept. of Mathematics, College of Science, Taibah University, Al-Madinah Al-Munawarah, Saudi Arabia.Dept. of Mathematics, Faculty of Sciences, University of Sfax, Tunisia. In this work, we define $\mathcal{Z}_{G}$ a topology on the vertex set of a graph $G$ which preserves the connectivity of the graph, called $\mathcal{Z}$-graphic topology. We prove that two isomorphic graphs have homeomorphic and symmetric $\mathcal{Z}$-graphic topologies. We show that $\mathcal{Z}_{G}$ is an Alexandroff topology and we give a necessary and sufficient condition for a topology to be $\mathcal{Z}$-graphic. https://journalskuwait.org/kjs/index.php/KJS/article/view/17541 |
| spellingShingle | Hanan Omer Zomam Makkia Dammak Z-graphic topology on undirected graph Kuwait Journal of Science |
| title | Z-graphic topology on undirected graph |
| title_full | Z-graphic topology on undirected graph |
| title_fullStr | Z-graphic topology on undirected graph |
| title_full_unstemmed | Z-graphic topology on undirected graph |
| title_short | Z-graphic topology on undirected graph |
| title_sort | z graphic topology on undirected graph |
| url | https://journalskuwait.org/kjs/index.php/KJS/article/view/17541 |
| work_keys_str_mv | AT hananomerzomam zgraphictopologyonundirectedgraph AT makkiadammak zgraphictopologyonundirectedgraph |