{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,5,9]],"date-time":"2025-05-09T15:32:52Z","timestamp":1746804772746,"version":"3.40.5"},"reference-count":18,"publisher":"Wiley","license":[{"start":{"date-parts":[[2013,1,1]],"date-time":"2013-01-01T00:00:00Z","timestamp":1356998400000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"funder":[{"name":"Slovak VEGA","award":["1\/0130\/12"],"award-info":[{"award-number":["1\/0130\/12"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Journal of Applied Mathematics"],"published-print":{"date-parts":[[2013]]},"abstract":"<jats:p>For a graph<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M2\"><mml:mi>G<\/mml:mi><mml:mo>=<\/mml:mo><mml:mrow><mml:mo stretchy=\"false\">(<\/mml:mo><mml:mrow><mml:mi>V<\/mml:mi><mml:mo>,<\/mml:mo><mml:mi>E<\/mml:mi><\/mml:mrow><mml:mo stretchy=\"false\">)<\/mml:mo><\/mml:mrow><\/mml:math>, a bijection<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<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M4\"><mml:mi>V<\/mml:mi><mml:mrow><mml:mo stretchy=\"false\">(<\/mml:mo><mml:mi>G<\/mml:mi><mml:mo stretchy=\"false\">)<\/mml:mo><\/mml:mrow><mml:mo>\u222a<\/mml:mo><mml:mi>E<\/mml:mi><mml:mrow><mml:mo stretchy=\"false\">(<\/mml:mo><mml:mi>G<\/mml:mi><mml:mo stretchy=\"false\">)<\/mml:mo><\/mml:mrow><mml:mo>\u2192<\/mml:mo><mml:mrow><mml:mo stretchy=\"false\">{<\/mml:mo><mml:mrow><mml:mn>1<\/mml:mn><mml:mo>,<\/mml:mo><mml:mn>2<\/mml:mn><mml:mo>,<\/mml:mo><mml:mn>\u2026<\/mml:mn><mml:mo>,<\/mml:mo><mml:mrow><mml:mo stretchy=\"false\">|<\/mml:mo><mml:mrow><mml:mi>V<\/mml:mi><mml:mrow><mml:mo stretchy=\"false\">(<\/mml:mo><mml:mi>G<\/mml:mi><mml:mo stretchy=\"false\">)<\/mml:mo><\/mml:mrow><\/mml:mrow><mml:mo stretchy=\"false\">|<\/mml:mo><\/mml:mrow><\/mml:mrow><\/mml:mrow><mml:mo>+<\/mml:mo><mml:mrow><mml:mrow><mml:mrow><mml:mo stretchy=\"false\">|<\/mml:mo><mml:mrow><mml:mi>E<\/mml:mi><mml:mrow><mml:mo stretchy=\"false\">(<\/mml:mo><mml:mi>G<\/mml:mi><mml:mo stretchy=\"false\">)<\/mml:mo><\/mml:mrow><\/mml:mrow><mml:mo stretchy=\"false\">|<\/mml:mo><\/mml:mrow><\/mml:mrow><mml:mo stretchy=\"false\">}<\/mml:mo><\/mml:mrow><\/mml:math>is called<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M5\"><mml:mrow><mml:mo stretchy=\"false\">(<\/mml:mo><mml:mrow><mml:mi>a<\/mml:mi><mml:mo>,<\/mml:mo><mml:mi>d<\/mml:mi><\/mml:mrow><mml:mo stretchy=\"false\">)<\/mml:mo><\/mml:mrow><\/mml:math>-edge-antimagic total (<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M6\"><mml:mrow><mml:mrow><mml:mrow><mml:mo stretchy=\"false\">(<\/mml:mo><mml:mrow><mml:mi>a<\/mml:mi><mml:mo>,<\/mml:mo><mml:mrow><mml:mi>d<\/mml:mi><mml:mo stretchy=\"false\">)<\/mml:mo><\/mml:mrow><\/mml:mrow><\/mml:mrow><\/mml:mrow><\/mml:mrow><\/mml:math>-EAT) labeling of<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M7\"><mml:mrow><mml:mi>G<\/mml:mi><\/mml:mrow><\/mml:math>if the edge-weights<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M8\"><mml:mi>w<\/mml:mi><mml:mrow><mml:mo stretchy=\"false\">(<\/mml:mo><mml:mrow><mml:mi>x<\/mml:mi><mml:mi>y<\/mml:mi><\/mml:mrow><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>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:mo>+<\/mml:mo><mml:mi>f<\/mml:mi><mml:mrow><mml:mo stretchy=\"false\">(<\/mml:mo><mml:mrow><mml:mi>x<\/mml:mi><mml:mi>y<\/mml:mi><\/mml:mrow><mml:mo stretchy=\"false\">)<\/mml:mo><\/mml:mrow><mml:mo>,<\/mml:mo><mml:mi>x<\/mml:mi><mml:mi>y<\/mml:mi><mml:mo>\u2208<\/mml:mo><mml:mi>E<\/mml:mi><mml:mrow><mml:mo stretchy=\"false\">(<\/mml:mo><mml:mi>G<\/mml:mi><mml:mo stretchy=\"false\">)<\/mml:mo><\/mml:mrow><\/mml:math>, form an arithmetic progression starting from<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M9\"><mml:mrow><mml:mi>a<\/mml:mi><\/mml:mrow><\/mml:math>and having a common difference<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M10\"><mml:mrow><mml:mi>d<\/mml:mi><\/mml:mrow><\/mml:math>, where<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M11\"><mml:mi>a<\/mml:mi><mml:mo>&gt;<\/mml:mo><mml:mn>0<\/mml:mn><\/mml:math>and<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M12\"><mml:mi>d<\/mml:mi><mml:mo>\u2265<\/mml:mo><mml:mn>0<\/mml:mn><\/mml:math>are two fixed integers. An<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M13\"><mml:mrow><mml:mo stretchy=\"false\">(<\/mml:mo><mml:mrow><mml:mi>a<\/mml:mi><mml:mo>,<\/mml:mo><mml:mi>d<\/mml:mi><\/mml:mrow><mml:mo stretchy=\"false\">)<\/mml:mo><\/mml:mrow><\/mml:math>-EAT labeling is called super<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M14\"><mml:mrow><mml:mo stretchy=\"false\">(<\/mml:mo><mml:mrow><mml:mi>a<\/mml:mi><mml:mo>,<\/mml:mo><mml:mi>d<\/mml:mi><\/mml:mrow><mml:mo stretchy=\"false\">)<\/mml:mo><\/mml:mrow><\/mml:math>-EAT labeling if the vertices are labeled with the smallest possible numbers; that is,<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M15\"><mml:mi>f<\/mml:mi><mml:mrow><mml:mo stretchy=\"false\">(<\/mml:mo><mml:mrow><mml:mi>V<\/mml:mi><\/mml:mrow><mml:mo stretchy=\"false\">)<\/mml:mo><\/mml:mrow><mml:mo>=<\/mml:mo><mml:mo stretchy=\"false\">{<\/mml:mo><mml:mn mathvariant=\"normal\">1,2<\/mml:mn><mml:mo>,<\/mml:mo><mml:mo>\u2026<\/mml:mo><mml:mo>,<\/mml:mo><mml:mo stretchy=\"false\">|<\/mml:mo><mml:mi>V<\/mml:mi><mml:mo stretchy=\"false\">(<\/mml:mo><mml:mi>G<\/mml:mi><mml:mo stretchy=\"false\">)<\/mml:mo><mml:mo stretchy=\"false\">|<\/mml:mo><mml:mo stretchy=\"false\">}<\/mml:mo><\/mml:math>. In this paper, we study super<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M16\"><mml:mrow><mml:mo stretchy=\"false\">(<\/mml:mo><mml:mrow><mml:mi>a<\/mml:mi><mml:mo>,<\/mml:mo><mml:mi>d<\/mml:mi><\/mml:mrow><mml:mo stretchy=\"false\">)<\/mml:mo><\/mml:mrow><\/mml:math>-EAT labeling of cycles with some pendant edges attached to different vertices of the cycle.<\/jats:p>","DOI":"10.1155\/2013\/896815","type":"journal-article","created":{"date-parts":[[2013,7,10]],"date-time":"2013-07-10T17:02:12Z","timestamp":1373475732000},"page":"1-6","source":"Crossref","is-referenced-by-count":1,"title":["On Super<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M1\"><mml:mrow><mml:mo stretchy=\"false\">(<\/mml:mo><mml:mrow><mml:mi>a<\/mml:mi><mml:mo>,<\/mml:mo><mml:mi>d<\/mml:mi><\/mml:mrow><mml:mo stretchy=\"false\">)<\/mml:mo><\/mml:mrow><\/mml:math>-Edge-Antimagic Total Labeling of Special Types of Crown Graphs"],"prefix":"10.1155","volume":"2013","author":[{"given":"Himayat","family":"Ullah","sequence":"first","affiliation":[{"name":"FAST-National University of Computer and Emerging Sciences, Peshawar 25000, Pakistan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Gohar","family":"Ali","sequence":"additional","affiliation":[{"name":"FAST-National University of Computer and Emerging Sciences, Peshawar 25000, Pakistan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Murtaza","family":"Ali","sequence":"additional","affiliation":[{"name":"FAST-National University of Computer and Emerging Sciences, Peshawar 25000, Pakistan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Andrea","family":"Semani\u010dov\u00e1-Fe\u0148ov\u010d\u00edkov\u00e1","sequence":"additional","affiliation":[{"name":"Department of Applied Mathematics and Informatics, Technical University, 042 00 Ko\u0161ice, Slovakia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","reference":[{"key":"18","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-0123-6"},{"year":"1996","key":"19"},{"year":"2008","key":"4"},{"volume":"18","journal-title":"The Electronic Journal of Combinatorics","year":"2011","key":"11"},{"issue":"2","key":"7","first-page":"105","volume":"34","year":"1998","journal-title":"SUT Journal of Mathematics"},{"key":"8","doi-asserted-by":"publisher","DOI":"10.1016\/S0012-365X(00)00314-9"},{"key":"13","doi-asserted-by":"crossref","first-page":"451","DOI":"10.4153\/CMB-1970-084-1","volume":"13","year":"1970","journal-title":"Canadian Mathematical Bulletin"},{"year":"1972","key":"14"},{"volume-title":"Arithmetisch antimagische graphen","year":"1993","key":"6"},{"year":"1990","key":"12"},{"key":"2","first-page":"229","volume":"60","year":"2001","journal-title":"Utilitas Mathematica"},{"key":"17","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-540-30540-8_19"},{"key":"15","first-page":"127","volume":"65","year":"2008","journal-title":"Journal of Combinatorial Mathematics and Combinatorial Computing"},{"key":"9","first-page":"199","volume":"26","year":"2002","journal-title":"The Australasian Journal of Combinatorics"},{"issue":"1","key":"3","first-page":"47","volume":"6","year":"2009","journal-title":"AKCE International Journal of Graphs and Combinatorics"},{"key":"10","first-page":"225","volume":"32","year":"2005","journal-title":"The Australasian Journal of Combinatorics"},{"key":"5"},{"key":"1","first-page":"193","volume":"79","year":"2009","journal-title":"Utilitas Mathematica"}],"container-title":["Journal of Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2013\/896815.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2013\/896815.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2013\/896815.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2017,6,21]],"date-time":"2017-06-21T12:03:34Z","timestamp":1498046614000},"score":1,"resource":{"primary":{"URL":"http:\/\/www.hindawi.com\/journals\/jam\/2013\/896815\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013]]},"references-count":18,"alternative-id":["896815","896815"],"URL":"https:\/\/doi.org\/10.1155\/2013\/896815","relation":{},"ISSN":["1110-757X","1687-0042"],"issn-type":[{"type":"print","value":"1110-757X"},{"type":"electronic","value":"1687-0042"}],"subject":[],"published":{"date-parts":[[2013]]}}}