{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,2]],"date-time":"2026-05-02T06:24:39Z","timestamp":1777703079861,"version":"3.51.4"},"reference-count":21,"publisher":"SAGE Publications","issue":"6","license":[{"start":{"date-parts":[[2019,5,23]],"date-time":"2019-05-23T00:00:00Z","timestamp":1558569600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/journals.sagepub.com\/page\/policies\/text-and-data-mining-license"}],"content-domain":{"domain":["journals.sagepub.com"],"crossmark-restriction":true},"short-container-title":["Journal of Intelligent &amp; Fuzzy Systems"],"published-print":{"date-parts":[[2019,6,11]]},"abstract":"<jats:p>\u00a0In this article, a technique to construct a new type of topological structures by graphs called topological graphs is introduced. We use the concept of a homeomorphism between topological graphs as a topological property to prove the isomorphic between graphs. We construct a computer program that builds graphs and its topological graphs. This model helps in studying many topological properties such as continuity, connectedness, compactness and separation axioms on graphs. Finally, we present some examples of different types of graphs and their topological graphs and study some of their topological and algebraic properties.<\/jats:p>","DOI":"10.3233\/jifs-171561","type":"journal-article","created":{"date-parts":[[2019,5,24]],"date-time":"2019-05-24T10:51:56Z","timestamp":1558695116000},"page":"5125-5134","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":11,"title":["New types of graphs induced by topological spaces"],"prefix":"10.1177","volume":"36","author":[{"given":"A.M.","family":"Kozae","sequence":"first","affiliation":[{"name":"Department of Mathematics, Faculty of Science, Tanta University, Tanta, Egypt"}]},{"given":"A.A.","family":"El Atik","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Science, Tanta University, Tanta, Egypt"}]},{"given":"A.","family":"Elrokh","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Computer Science, Faculty of Science, Menoufia University, Menoufia, Egypt"}]},{"given":"M.","family":"Atef","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Computer Science, Faculty of Science, Menoufia University, Menoufia, Egypt"}]}],"member":"179","published-online":{"date-parts":[[2019,5,23]]},"reference":[{"key":"e_1_3_2_2_2","doi-asserted-by":"crossref","unstructured":"AkramM. m-Polar Fuzzy Graphs Studies in Fuzziness and Soft Computing Springer 2019.","DOI":"10.1007\/978-3-030-03751-2"},{"key":"e_1_3_2_3_2","doi-asserted-by":"crossref","unstructured":"Bondy A.J. Murty R.S.U. Graph theory with applications Elsevier Science Publishing Company Inc 1975.","DOI":"10.1007\/978-1-349-03521-2"},{"key":"e_1_3_2_4_2","unstructured":"Cain L.G. Introduction to general Addison Wesley Publishing Company Inc 1994."},{"key":"e_1_3_2_5_2","unstructured":"DiestelR. Graph theory II Heidelberg Springer-Verlag IV 2010."},{"key":"e_1_3_2_6_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.chaos.2006.04.043"},{"key":"e_1_3_2_7_2","doi-asserted-by":"publisher","DOI":"10.1142\/S1793524516500546"},{"key":"e_1_3_2_8_2","doi-asserted-by":"publisher","DOI":"10.1142\/S1793524518500584"},{"key":"e_1_3_2_9_2","doi-asserted-by":"publisher","DOI":"10.1142\/S1793524516500595"},{"key":"e_1_3_2_10_2","doi-asserted-by":"publisher","DOI":"10.1109\/TFUZZ.2018.2883023"},{"key":"e_1_3_2_11_2","doi-asserted-by":"crossref","unstructured":"Chartrand G. Lesniak L. Zhang P. Textbooks in Mathematics(Graphs and Digraphs) Sixth Edition 2016.","DOI":"10.1201\/b19731"},{"key":"e_1_3_2_12_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0304-3975(02)00701-6"},{"key":"e_1_3_2_13_2","doi-asserted-by":"publisher","DOI":"10.1002\/mma.4726"},{"key":"e_1_3_2_14_2","doi-asserted-by":"publisher","DOI":"10.1142\/S1793524519500062"},{"key":"e_1_3_2_15_2","unstructured":"RamjiL. Algebra 1 Groups Rings Fields and Arithmetic Springer Nature Singapore Pte Ltd 2017."},{"key":"e_1_3_2_16_2","doi-asserted-by":"publisher","DOI":"10.1021\/ci0100898"},{"key":"e_1_3_2_17_2","unstructured":"Morris S.A. Topology without tears version of March 1 2017."},{"key":"e_1_3_2_18_2","first-page":"1103","article-title":"Topological properties on graph VS medical application in human heart","volume":"15","author":"Shokry M.","year":"2013","unstructured":"ShokryM., AlyR.E., Topological properties on graph VS medical application in human heart, International Journal of Applied Mathematics 15 (2013), 1103\u20131109.","journal-title":"International Journal of Applied Mathematics"},{"key":"e_1_3_2_19_2","unstructured":"Wilson R.J. Rough sets Introduction to graph theory Fourth Edition Longmon Maleysia 1996."},{"key":"e_1_3_2_20_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.ins.2018.10.016"},{"key":"e_1_3_2_21_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.cie.2019.01.004"},{"key":"e_1_3_2_22_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.ins.2018.11.033"}],"container-title":["Journal of Intelligent &amp; Fuzzy Systems"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/JIFS-171561","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/full-xml\/10.3233\/JIFS-171561","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/JIFS-171561","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,29]],"date-time":"2026-04-29T09:37:47Z","timestamp":1777455467000},"score":1,"resource":{"primary":{"URL":"https:\/\/journals.sagepub.com\/doi\/10.3233\/JIFS-171561"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,5,23]]},"references-count":21,"journal-issue":{"issue":"6","published-print":{"date-parts":[[2019,6,11]]}},"alternative-id":["10.3233\/JIFS-171561"],"URL":"https:\/\/doi.org\/10.3233\/jifs-171561","relation":{},"ISSN":["1064-1246","1875-8967"],"issn-type":[{"value":"1064-1246","type":"print"},{"value":"1875-8967","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,5,23]]}}}