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Intuitionistic fuzzy graphs (IFG\n                    <jats:italic>s<\/jats:italic>\n                    ) are a convenient tool to represent the objects and relations between them with two types of information using truth membership degree and falsity membership degree. This research work presents the concept of  under the structure IFG\n                    <jats:italic>s<\/jats:italic>\n                    ,\n                    <jats:italic>I<\/jats:italic>\n                    <jats:italic>F<\/jats:italic>\n                    trees, and\n                    <jats:italic>I<\/jats:italic>\n                    <jats:italic>F<\/jats:italic>\n                    cycles. Some bounds on  are investigated. The relationship between  and connectivity index  is also studied. In the end of this study, an application of the  in transport network flow is proposed.\n                  <\/jats:p>","DOI":"10.1155\/2022\/8016096","type":"journal-article","created":{"date-parts":[[2022,5,15]],"date-time":"2022-05-15T01:50:05Z","timestamp":1652579405000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Wiener Index of Intuitionistic Fuzzy Graphs with an Application to Transport Network Flow"],"prefix":"10.1155","volume":"2022","author":[{"given":"Tulat","family":"Naeem","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5715-9299","authenticated-orcid":false,"given":"Muhammad Kamran","family":"Jamil","sequence":"additional","affiliation":[]},{"given":"Khawaja Muhammad","family":"Fahd","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9920-4892","authenticated-orcid":false,"given":"Abdu","family":"alAmeri","sequence":"additional","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2022,5,14]]},"reference":[{"key":"e_1_2_9_1_2","doi-asserted-by":"publisher","DOI":"10.1016\/s0019-9958(65)90241-x"},{"key":"e_1_2_9_2_2","doi-asserted-by":"publisher","DOI":"10.1016\/0022-247x(67)90189-8"},{"key":"e_1_2_9_3_2","doi-asserted-by":"publisher","DOI":"10.1287\/mnsc.17.4.b141"},{"key":"e_1_2_9_4_2","unstructured":"SambucR. 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