{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,2]],"date-time":"2026-05-02T06:51:11Z","timestamp":1777704671424,"version":"3.51.4"},"reference-count":37,"publisher":"SAGE Publications","issue":"6","license":[{"start":{"date-parts":[[2018,11,14]],"date-time":"2018-11-14T00:00:00Z","timestamp":1542153600000},"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":[[2018,12,24]]},"abstract":"<jats:p>\n                    In this article, a new idea of fuzzy coloring of\n                    <jats:italic>m<\/jats:italic>\n                    -polar fuzzy graph is presented while establishing the relationship between chromatic number of\n                    <jats:italic>m<\/jats:italic>\n                    -polar fuzzy graph and it\u2019s underlying crisp graph. Some properties of\n                    <jats:italic>m<\/jats:italic>\n                    -polar fuzzy graph and new concepts of independently strong edge and independently weak edge in\n                    <jats:italic>m<\/jats:italic>\n                    -polar fuzzy graph are proved. The differences between fuzzy coloring of fuzzy graph and\n                    <jats:italic>m<\/jats:italic>\n                    -polar fuzzy graph are discussed. It is also shown that a\n                    <jats:italic>m<\/jats:italic>\n                    -polar fuzzy graph can be decomposed into\n                    <jats:italic>m<\/jats:italic>\n                    fuzzy graphs. Again, from\n                    <jats:italic>m<\/jats:italic>\n                    isomorphic fuzzy graph one can construct a\n                    <jats:italic>m<\/jats:italic>\n                    -polar fuzzy graph. A relation among chromatic numbers of\n                    <jats:italic>m<\/jats:italic>\n                    -polar fuzzy graph and\n                    <jats:italic>m<\/jats:italic>\n                    such graphs is established. Lastly a real life application of the fuzzy coloring is discussed.\n                  <\/jats:p>","DOI":"10.3233\/jifs-181262","type":"journal-article","created":{"date-parts":[[2018,11,16]],"date-time":"2018-11-16T12:59:02Z","timestamp":1542373142000},"page":"6379-6391","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":23,"title":["Fuzzy colouring of\n                    <i>m<\/i>\n                    -polar fuzzy graph and its application"],"prefix":"10.1177","volume":"35","author":[{"given":"Tanmoy","family":"Mahapatra","sequence":"first","affiliation":[{"name":"Department of Applied Mathematics with Oceanology and Computer Programming, Vidyasagar University, Midnapore, India"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Madhumangal","family":"Pal","sequence":"additional","affiliation":[{"name":"Department of Applied Mathematics with Oceanology and Computer Programming, Vidyasagar University, Midnapore, India"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"179","published-online":{"date-parts":[[2018,11,14]]},"reference":[{"issue":"10","key":"e_1_3_2_2_2","first-page":"23","article-title":"Fuzzy graph coloring using a-cut","volume":"4","author":"Ananthanarayanan M.","year":"2014","unstructured":"M.Ananthanarayanan and S.Lavanya, Fuzzy graph coloring using a-cut, International Journal of Engineering and Applied Sciences 4(10) (2014), 23\u201328.","journal-title":"International Journal of Engineering and Applied Sciences"},{"key":"e_1_3_2_3_2","doi-asserted-by":"publisher","DOI":"10.1080\/09720529.2015.1117221"},{"key":"e_1_3_2_4_2","article-title":"Certain types of edge m-polar fuzzy graph","author":"Akram M.","year":"2016","unstructured":"M.Akram, N.Wassem and W.A.Dudek, Certain types of edge m-polar fuzzy graph, Iran J Fuzzy Syst (2016). 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