{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,7,5]],"date-time":"2023-07-05T13:13:50Z","timestamp":1688562830280},"reference-count":15,"publisher":"World Scientific Pub Co Pte Lt","issue":"03","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Discrete Math. Algorithm. Appl."],"published-print":{"date-parts":[[2009,9]]},"abstract":"<jats:p> A graph G = (V(G), E(G)) with q edges is said to be odd graceful if there exists an injection f from V(G) to {0, 1, 2, \u2026, 2q - 1} such that the edge labeling set is {1, 3, 5, \u2026, 2q - 1} with each edge xy assigned the label |f(x) - f(y)|. In this paper, we prove that P<jats:sub>n<\/jats:sub> \u00d7 P<jats:sub>m<\/jats:sub> (m = 2, 3, 4), generalized crown graphs C<jats:sub>n<\/jats:sub> \u2299 K<jats:sub>1,t<\/jats:sub> and gear graphs are odd graceful. <\/jats:p>","DOI":"10.1142\/s1793830909000300","type":"journal-article","created":{"date-parts":[[2009,9,30]],"date-time":"2009-09-30T07:00:24Z","timestamp":1254294024000},"page":"377-388","source":"Crossref","is-referenced-by-count":1,"title":["ODD GRACEFUL LABELINGS OF GRAPHS"],"prefix":"10.1142","volume":"01","author":[{"given":"ZHEN-BIN","family":"GAO","sequence":"first","affiliation":[{"name":"College of Science, Harbin Engineering University, Harbin, 150001, P. R. China"}]},{"given":"XIAO-DONG","family":"ZHANG","sequence":"additional","affiliation":[{"name":"Department of Math., Shanghai Jiaotong University, Shanghai, 200240, P. R. China"}]},{"given":"LI-JUAN","family":"XU","sequence":"additional","affiliation":[{"name":"College of Science, Harbin Engineering University, Harbin, 150001, P. R. China"}]}],"member":"219","published-online":{"date-parts":[[2012,4,5]]},"reference":[{"key":"rf1","first-page":"445","volume":"65","author":"Acharya M.","journal-title":"Ars Combin."},{"key":"rf2","first-page":"81","volume":"23","author":"Acharya B. D.","journal-title":"Indian J. Math."},{"key":"rf3","first-page":"233","volume":"39","author":"Ba\u010da M.","journal-title":"Math., Slovaca"},{"key":"rf4","first-page":"139","volume":"41","author":"Barrientos C.","journal-title":"J. Combin. Math. Combin. Comput."},{"key":"rf6","first-page":"105","volume":"34","author":"Enomoto H.","journal-title":"SUT J. Math."},{"key":"rf7","doi-asserted-by":"publisher","DOI":"10.1016\/S0012-365X(00)00314-9"},{"key":"rf8","first-page":"#DS6","volume":"15","author":"Gallian J. A.","journal-title":"Electro. J. Combin."},{"key":"rf10","first-page":"35","volume":"24","author":"Gao Z.-B.","journal-title":"J. Natural Sci. Heilongjiang Univ."},{"key":"rf12","doi-asserted-by":"publisher","DOI":"10.1137\/0601045"},{"key":"rf13","doi-asserted-by":"publisher","DOI":"10.1002\/nav.20041"},{"key":"rf14","first-page":"167","volume":"34","author":"Jungreis D.","journal-title":"Ars Combin."},{"key":"rf15","first-page":"193","volume":"45","author":"Kong M. C.","journal-title":"Ars Combin."},{"key":"rf16","first-page":"231","volume":"50","author":"Lo S.","journal-title":"Congress Numer."},{"key":"rf17","first-page":"15","volume":"4","author":"Ma K. J.","journal-title":"J. Math. Res. Expo."},{"key":"rf18","first-page":"167","volume":"29","author":"Maheo M.","journal-title":"Discrete Math."}],"container-title":["Discrete Mathematics, Algorithms and Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S1793830909000300","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,7]],"date-time":"2019-08-07T01:29:15Z","timestamp":1565141355000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S1793830909000300"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2009,9]]},"references-count":15,"journal-issue":{"issue":"03","published-online":{"date-parts":[[2012,4,5]]},"published-print":{"date-parts":[[2009,9]]}},"alternative-id":["10.1142\/S1793830909000300"],"URL":"https:\/\/doi.org\/10.1142\/s1793830909000300","relation":{},"ISSN":["1793-8309","1793-8317"],"issn-type":[{"value":"1793-8309","type":"print"},{"value":"1793-8317","type":"electronic"}],"subject":[],"published":{"date-parts":[[2009,9]]}}}