{"title":"无向图上的z图拓扑","authors":"H. O. Zomam, M. Dammak","doi":"10.48129/kjs.17541","DOIUrl":null,"url":null,"abstract":"In this work, we define ZG a topology on the vertex set of a graph G which preserves the connectivity of the graph, called Z-graphic topology. We prove that two isomorphic graphs have homeomorphic and symmetric Z-graphic topologies. We show that ZG is an Alexandroff topology and we give a necessary and sufficient condition for a topology to be Z-graphic.","PeriodicalId":49933,"journal":{"name":"Kuwait Journal of Science & Engineering","volume":"1 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2022-05-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"Z-graphic topology on undirected graph\",\"authors\":\"H. O. Zomam, M. Dammak\",\"doi\":\"10.48129/kjs.17541\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this work, we define ZG a topology on the vertex set of a graph G which preserves the connectivity of the graph, called Z-graphic topology. We prove that two isomorphic graphs have homeomorphic and symmetric Z-graphic topologies. We show that ZG is an Alexandroff topology and we give a necessary and sufficient condition for a topology to be Z-graphic.\",\"PeriodicalId\":49933,\"journal\":{\"name\":\"Kuwait Journal of Science & Engineering\",\"volume\":\"1 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2022-05-10\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Kuwait Journal of Science & Engineering\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.48129/kjs.17541\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Kuwait Journal of Science & Engineering","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.48129/kjs.17541","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
In this work, we define ZG a topology on the vertex set of a graph G which preserves the connectivity of the graph, called Z-graphic topology. We prove that two isomorphic graphs have homeomorphic and symmetric Z-graphic topologies. We show that ZG is an Alexandroff topology and we give a necessary and sufficient condition for a topology to be Z-graphic.
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