{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,7]],"date-time":"2026-05-07T11:43:45Z","timestamp":1778154225652,"version":"3.51.4"},"reference-count":12,"publisher":"Wiley","license":[{"start":{"date-parts":[[2014,1,1]],"date-time":"2014-01-01T00:00:00Z","timestamp":1388534400000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"funder":[{"DOI":"10.13039\/501100006109","name":"VEGA","doi-asserted-by":"crossref","award":["1\/0130\/12"],"award-info":[{"award-number":["1\/0130\/12"]}],"id":[{"id":"10.13039\/501100006109","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Journal of Applied Mathematics"],"published-print":{"date-parts":[[2014]]},"abstract":"<jats:p>A graph<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M1\"><mml:mrow><mml:mi>G<\/mml:mi><\/mml:mrow><\/mml:math>with<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M2\"><mml:mrow><mml:mi>q<\/mml:mi><\/mml:mrow><\/mml:math>edges is said to be harmonious, if there is an injection<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M3\"><mml:mrow><mml:mi>f<\/mml:mi><\/mml:mrow><\/mml:math>from the vertices of<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M4\"><mml:mrow><mml:mi>G<\/mml:mi><\/mml:mrow><\/mml:math>to the group of integers modulo<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M5\"><mml:mrow><mml:mi>q<\/mml:mi><\/mml:mrow><\/mml:math>such that when each edge<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M6\"><mml:mi>x<\/mml:mi><mml:mi>y<\/mml:mi><\/mml:math>is assigned the label<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M7\"><mml:mi>f<\/mml:mi><mml:mrow><mml:mo stretchy=\"false\">(<\/mml:mo><mml:mi>x<\/mml:mi><mml:mo stretchy=\"false\">)<\/mml:mo><\/mml:mrow><mml:mo>+<\/mml:mo><mml:mi>f<\/mml:mi><mml:mrow><mml:mo stretchy=\"false\">(<\/mml:mo><mml:mi>y<\/mml:mi><mml:mo stretchy=\"false\">)<\/mml:mo><\/mml:mrow><\/mml:math>(mod<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M8\"><mml:mrow><mml:mi>q<\/mml:mi><\/mml:mrow><\/mml:math>), the resulting edge labels are distinct. In this paper, we study the existence of harmonious labeling for the corona graphs of a cycle and a graph<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M9\"><mml:mrow><mml:mi>G<\/mml:mi><\/mml:mrow><\/mml:math>and for the corona graph of<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M10\"><mml:mrow><mml:msub><mml:mi>K<\/mml:mi><mml:mn>2<\/mml:mn><\/mml:msub><\/mml:mrow><\/mml:math>and a tree.<\/jats:p>","DOI":"10.1155\/2014\/627248","type":"journal-article","created":{"date-parts":[[2014,4,3]],"date-time":"2014-04-03T17:07:30Z","timestamp":1396544850000},"page":"1-4","source":"Crossref","is-referenced-by-count":4,"title":["On Harmonious Labeling of Corona Graphs"],"prefix":"10.1155","volume":"2014","author":[{"given":"Martin","family":"Ba\u010da","sequence":"first","affiliation":[{"name":"Department of Applied Mathematics and Informatics, Technical University, 042 00 Ko\u0161ice, Slovakia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Maged Z.","family":"Youssef","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Statistics, College of Sciences, Al-Imam Mohammed Ibn Saud Islamic University, Riyadh 11623, Saudi Arabia"},{"name":"Department of Mathematics, Faculty of Science, Ain Shams University, Abbassia, Cairo 11566, Egypt"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","reference":[{"key":"1","doi-asserted-by":"publisher","DOI":"10.1137\/0601045"},{"key":"2","first-page":"181","volume":"32","year":"1981","journal-title":"Congressus Numerantium"},{"key":"4","doi-asserted-by":"publisher","DOI":"10.1002\/jgt.3190070208"},{"key":"5","first-page":"1","volume":"19","year":"2012","journal-title":"The Electronic Journal of Combinatorics"},{"key":"6","doi-asserted-by":"publisher","DOI":"10.1155\/2013\/896815"},{"key":"7","doi-asserted-by":"publisher","DOI":"10.1007\/BF01844162"},{"issue":"4","key":"8","first-page":"325","volume":"2","year":"1989","journal-title":"Systems Science and Mathematical Sciences"},{"issue":"1","key":"9","first-page":"125","volume":"16","year":"1996","journal-title":"Hunan Annals of Mathematics"},{"issue":"9-10","key":"10","first-page":"243","volume":"16","year":"1993","journal-title":"National Academy Science Letters"},{"key":"11","doi-asserted-by":"publisher","DOI":"10.1007\/s003730050026"},{"key":"12","first-page":"269","volume":"28","year":"2005","journal-title":"National Academy Science Letters"},{"key":"13","first-page":"237","volume":"23","year":"1987","journal-title":"Ars Combinatoria"}],"container-title":["Journal of Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2014\/627248.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2014\/627248.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2014\/627248.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2016,8,18]],"date-time":"2016-08-18T18:41:14Z","timestamp":1471545674000},"score":1,"resource":{"primary":{"URL":"http:\/\/www.hindawi.com\/journals\/jam\/2014\/627248\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014]]},"references-count":12,"alternative-id":["627248","627248"],"URL":"https:\/\/doi.org\/10.1155\/2014\/627248","relation":{},"ISSN":["1110-757X","1687-0042"],"issn-type":[{"value":"1110-757X","type":"print"},{"value":"1687-0042","type":"electronic"}],"subject":[],"published":{"date-parts":[[2014]]}}}