{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,8]],"date-time":"2025-12-08T22:46:00Z","timestamp":1765233960121,"version":"build-2065373602"},"reference-count":25,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2025,1,23]],"date-time":"2025-01-23T00:00:00Z","timestamp":1737590400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Deanship of Scientific Research at the University of Ha\u2019il\u2014Saudi Arabia","award":["RG-24 104"],"award-info":[{"award-number":["RG-24 104"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>In this work, we use the monophonic eccentric open neighborhood system and the upper approximation neighborhood system to construct a new class of topologies in the theory of undirected simple graphs. We study some fundamental topological properties of this class and characterize the graphs that induce the indiscrete or discrete topology. Next, we present the openness, the connectedness and the continuity properties with isomorphic maps of graphs. Some applications concerning the topological discrete and connectedness properties for some corresponding graphs of the COVID-19 form and its diffusion are introduced.<\/jats:p>","DOI":"10.3390\/axioms14020084","type":"journal-article","created":{"date-parts":[[2025,1,23]],"date-time":"2025-01-23T12:24:09Z","timestamp":1737635049000},"page":"84","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Upper a-Graphical Topological Spaces with the COVID-19 Form and Its Diffusion"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0009-0009-4773-7046","authenticated-orcid":false,"given":"Faten H.","family":"Damag","sequence":"first","affiliation":[{"name":"Department of Mathematics, Faculty of Sciences, University of Ha\u2019il, Ha\u2019il 2440, Saudi Arabia"}]},{"given":"Amin","family":"Saif","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Sciences, University of Ha\u2019il, Ha\u2019il 2440, Saudi Arabia"},{"name":"Department of Mathematics, Faculty of Applied Sciences, Taiz University, Taiz 9674, Yemen"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1217-963X","authenticated-orcid":false,"given":"Adem","family":"Kili\u00e7man","sequence":"additional","affiliation":[{"name":"School of Mathematical Sciences, College of Computing, Informatics and Mathematics, Universiti Teknologi MARA, Shah Alam 40450, Selangor, Malaysia"}]},{"given":"Mouataz Billah","family":"Mesmouli","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Sciences, University of Ha\u2019il, Ha\u2019il 2440, Saudi Arabia"}]},{"given":"Fozaiyah","family":"Alhubairah","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Sciences, University of Ha\u2019il, Ha\u2019il 2440, Saudi Arabia"}]}],"member":"1968","published-online":{"date-parts":[[2025,1,23]]},"reference":[{"key":"ref_1","first-page":"647","article-title":"An Alexandroff topology on graphs","volume":"39","author":"Jafarian","year":"2013","journal-title":"Bull. 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