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If such a coloring exists, the number of distinct [Formula: see text]-colorings and chromatic number in the given fuzzy graph can be obtained. As an application, we analyze the traffic lights problem by using this method. <\/jats:p>","DOI":"10.1142\/s179300572450025x","type":"journal-article","created":{"date-parts":[[2023,5,14]],"date-time":"2023-05-14T10:11:09Z","timestamp":1684059069000},"page":"473-486","source":"Crossref","is-referenced-by-count":0,"title":["Fuzzy Graph Coloring Using Gr\u00f6bner Basis"],"prefix":"10.1142","volume":"20","author":[{"given":"Hossein","family":"Jafari","sequence":"first","affiliation":[{"name":"Department of Mathematics, Chabahar Maritime University, Iran"}]},{"given":"Hamed","family":"Farahani","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Chabahar Maritime University, Iran"}]}],"member":"219","published-online":{"date-parts":[[2023,7,7]]},"reference":[{"key":"S179300572450025XBIB001","doi-asserted-by":"publisher","DOI":"10.1016\/j.amc.2006.04.063"},{"key":"S179300572450025XBIB002","doi-asserted-by":"publisher","DOI":"10.1016\/j.cor.2005.09.010"},{"key":"S179300572450025XBIB003","doi-asserted-by":"publisher","DOI":"10.1016\/j.cor.2010.04.012"},{"volume-title":"Graph Theory: An Algorithmic Approach","year":"1975","author":"Christofides N.","key":"S179300572450025XBIB004"},{"key":"S179300572450025XBIB005","doi-asserted-by":"publisher","DOI":"10.1016\/S0304-3975(01)00164-5"},{"key":"S179300572450025XBIB006","doi-asserted-by":"publisher","DOI":"10.1016\/0165-0114(92)90369-F"},{"key":"S179300572450025XBIB007","doi-asserted-by":"publisher","DOI":"10.1016\/j.protcy.2012.05.042"},{"key":"S179300572450025XBIB008","doi-asserted-by":"publisher","DOI":"10.1016\/S0304-3975(00)00231-0"},{"key":"S179300572450025XBIB009","doi-asserted-by":"publisher","DOI":"10.1016\/j.omega.2004.04.006"},{"key":"S179300572450025XBIB010","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-7908-1854-3"},{"key":"S179300572450025XBIB011","doi-asserted-by":"publisher","DOI":"10.1109\/FUZZ.2001.1008846"},{"volume-title":"Introduction to Combinat6orial Mathematics","year":"1968","author":"Liu C. 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