{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,5,9]],"date-time":"2025-05-09T15:08:40Z","timestamp":1746803320622,"version":"3.40.5"},"reference-count":11,"publisher":"Wiley","license":[{"start":{"date-parts":[[2017,1,1]],"date-time":"2017-01-01T00:00:00Z","timestamp":1483228800000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Advances in Fuzzy Systems"],"published-print":{"date-parts":[[2017]]},"abstract":"<jats:p>The main purpose of this paper is to introduce the notion of <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M2\"><mml:mrow><mml:mi>m<\/mml:mi><\/mml:mrow><\/mml:math>-polar <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M3\"><mml:mrow><mml:mi>h<\/mml:mi><\/mml:mrow><\/mml:math>-morphism on <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M4\"><mml:mrow><mml:mi>m<\/mml:mi><\/mml:mrow><\/mml:math>-polar fuzzy graphs. The action of <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M5\"><mml:mrow><mml:mi>m<\/mml:mi><\/mml:mrow><\/mml:math>-polar <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M6\"><mml:mrow><mml:mi>h<\/mml:mi><\/mml:mrow><\/mml:math>-morphism on <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M7\"><mml:mrow><mml:mi>m<\/mml:mi><\/mml:mrow><\/mml:math>-polar fuzzy graphs is studied. Some elegant theorems on weak and coweak isomorphism are obtained. Also, some properties of highly irregular, edge regular, and totally edge regular <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M8\"><mml:mrow><mml:mi>m<\/mml:mi><\/mml:mrow><\/mml:math>-polar fuzzy graphs are studied.<\/jats:p>","DOI":"10.1155\/2017\/4715421","type":"journal-article","created":{"date-parts":[[2017,8,23]],"date-time":"2017-08-23T17:01:47Z","timestamp":1503507707000},"page":"1-9","source":"Crossref","is-referenced-by-count":10,"title":["Morphism of <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M1\"><mml:mrow><mml:mi>m<\/mml:mi><\/mml:mrow><\/mml:math>-Polar Fuzzy Graph"],"prefix":"10.1155","volume":"2017","author":[{"given":"Ch.","family":"Ramprasad","sequence":"first","affiliation":[{"name":"Department of Mathematics, Vasireddy Venkatadri Institute of Technology, Nambur 522 508, India"},{"name":"Department of Mathematics, VFSTR University, Vadlamudi 522 237, India"}]},{"given":"P. L. 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