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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Main Authors: Hanan Omer Zomam, Makkia Dammak
Format: Article
Language:English
Published: Elsevier 2023-03-01
Series:Kuwait Journal of Science
Online Access:https://journalskuwait.org/kjs/index.php/KJS/article/view/17541
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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.
format Article
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institution DOAJ
issn 2307-4108
2307-4116
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publishDate 2023-03-01
publisher Elsevier
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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