{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,5,14]],"date-time":"2025-05-14T02:52:23Z","timestamp":1747191143683,"version":"3.40.5"},"reference-count":24,"publisher":"Wiley","license":[{"start":{"date-parts":[[2022,6,28]],"date-time":"2022-06-28T00:00:00Z","timestamp":1656374400000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["International Journal of Mathematics and Mathematical Sciences"],"published-print":{"date-parts":[[2022,6,28]]},"abstract":"<jats:p>The article describes a new thought on the chromatic polynomial of an intuitionistic fuzzy graph which is illustrated based on <jats:inline-formula>\n                     <a:math xmlns:a=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M2\">\n                        <a:mfenced open=\"(\" close=\")\" separators=\"|\">\n                           <a:mrow>\n                              <a:mi>\u03b1<\/a:mi>\n                              <a:mo>,<\/a:mo>\n                              <a:mi>\u03b2<\/a:mi>\n                           <\/a:mrow>\n                        <\/a:mfenced>\n                     <\/a:math>\n                  <\/jats:inline-formula>-level graphs. Besides, the alpha-beta fundamental set of an intuitionistic fuzzy graph is also defined with a vivid description. In addition to that, some characterizations of the chromatic polynomial of an intuitionistic fuzzy graph are specified as well verified. Furthermore, some untouched properties of the <jats:inline-formula>\n                     <f:math xmlns:f=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M3\">\n                        <f:mfenced open=\"(\" close=\")\" separators=\"|\">\n                           <f:mrow>\n                              <f:mi>\u03b1<\/f:mi>\n                              <f:mo>,<\/f:mo>\n                              <f:mi>\u03b2<\/f:mi>\n                           <\/f:mrow>\n                        <\/f:mfenced>\n                     <\/f:math>\n                  <\/jats:inline-formula>-level graph are also projected and proved.<\/jats:p>","DOI":"10.1155\/2022\/9320700","type":"journal-article","created":{"date-parts":[[2022,6,28]],"date-time":"2022-06-28T18:36:54Z","timestamp":1656441414000},"page":"1-7","source":"Crossref","is-referenced-by-count":3,"title":["Chromatic Polynomial of Intuitionistic Fuzzy Graphs Using <a:math xmlns:a=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M1\">\n                     <a:mfenced open=\"(\" close=\")\" separators=\"|\">\n                        <a:mrow>\n                           <a:mi>\u03b1<\/a:mi>\n                           <a:mo>,<\/a:mo>\n                           <a:mi>\u03b2<\/a:mi>\n                        <\/a:mrow>\n                     <\/a:mfenced>\n                  <\/a:math>-Levels"],"prefix":"10.1155","volume":"2022","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-3094-1170","authenticated-orcid":true,"given":"V. N. SrinivasaRao","family":"Repalle","sequence":"first","affiliation":[{"name":"Department of Mathematics, College of Natural and Computational Sciences, Wollega University, Nekemte, Ethiopia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1719-2275","authenticated-orcid":true,"given":"Lateram Zawuga","family":"Hordofa","sequence":"additional","affiliation":[{"name":"Department of Mathematics, College of Natural and Computational Sciences, Wollega University, Nekemte, Ethiopia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8096-0893","authenticated-orcid":true,"given":"Mamo Abebe","family":"Ashebo","sequence":"additional","affiliation":[{"name":"Department of Mathematics, College of Natural and Computational Sciences, Wollega University, Nekemte, Ethiopia"}]}],"member":"311","reference":[{"key":"1","doi-asserted-by":"publisher","DOI":"10.1109\/PERCOMW.2006.129"},{"issue":"3","key":"2","first-page":"124","article-title":"Uses of Graph Theory in a day to day life","volume":"7","author":"V. 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