{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,28]],"date-time":"2025-09-28T12:50:41Z","timestamp":1759063841074},"reference-count":14,"publisher":"World Scientific Pub Co Pte Lt","issue":"04","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Discrete Math. Algorithm. Appl."],"published-print":{"date-parts":[[2012,12]]},"abstract":"<jats:p> A proper [k]-edge coloring of a graph G is a proper edge coloring of G using colors of the set [k] = {1, 2,\u2026,k}. A neighbor sum distinguishing [k]-edge coloring of G is a proper [k]-edge coloring of G such that for each edge uv \u2208 E(G), the sum of colors taken on the edges incident to u is different from the sum of colors taken on the edges incident to v. By ndi<jats:sub>\u03a3<\/jats:sub>(G), we denote the smallest value k in such a coloring of G. In this paper, we obtain that (1) ndi<jats:sub>\u03a3<\/jats:sub>(G) \u2264 max {2\u0394(G) + 1, 25} if G is a planar graph, (2) ndi<jats:sub>\u03a3<\/jats:sub>(G) \u2264 max {2\u0394(G), 19} if G is a graph such that mad(G) \u2264 5. <\/jats:p>","DOI":"10.1142\/s1793830912500474","type":"journal-article","created":{"date-parts":[[2012,9,25]],"date-time":"2012-09-25T15:17:45Z","timestamp":1348586265000},"page":"1250047","source":"Crossref","is-referenced-by-count":21,"title":["NEIGHBOR SUM DISTINGUISHING COLORING OF SOME GRAPHS"],"prefix":"10.1142","volume":"04","author":[{"given":"AIJUN","family":"DONG","sequence":"first","affiliation":[{"name":"School of Science, Shandong Jiao Tong University, Jinan, 250023, P. R. China"}]},{"given":"GUANGHUI","family":"WANG","sequence":"additional","affiliation":[{"name":"School of Mathematics, Shandong University, Jinan, 250100, P. R. China"}]}],"member":"219","published-online":{"date-parts":[[2013,1,4]]},"reference":[{"key":"rf1","doi-asserted-by":"publisher","DOI":"10.1007\/s00493-007-0041-6"},{"key":"rf2","doi-asserted-by":"publisher","DOI":"10.1016\/j.dam.2007.05.059"},{"key":"rf3","doi-asserted-by":"publisher","DOI":"10.1016\/j.disc.2004.12.027"},{"key":"rf4","doi-asserted-by":"publisher","DOI":"10.1137\/S0895480102414107"},{"key":"rf5","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-349-03521-2"},{"key":"rf6","doi-asserted-by":"publisher","DOI":"10.1007\/s00373-006-0671-2"},{"key":"rf7","author":"Flandrin E.","journal-title":"Graph. Combinator."},{"key":"rf8","doi-asserted-by":"publisher","DOI":"10.1016\/j.jctb.2005.04.002"},{"key":"rf9","doi-asserted-by":"publisher","DOI":"10.1016\/j.jctb.2009.06.002"},{"key":"rf10","doi-asserted-by":"publisher","DOI":"10.1016\/j.jctb.2003.12.001"},{"key":"rf11","doi-asserted-by":"publisher","DOI":"10.1002\/jgt.10077"},{"key":"rf12","doi-asserted-by":"publisher","DOI":"10.1007\/s10878-008-9178-5"},{"key":"rf13","doi-asserted-by":"publisher","DOI":"10.1007\/s11464-008-0041-x"},{"key":"rf14","doi-asserted-by":"publisher","DOI":"10.1016\/S0893-9659(02)80015-5"}],"container-title":["Discrete Mathematics, Algorithms and Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S1793830912500474","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,6]],"date-time":"2019-08-06T17:14:15Z","timestamp":1565111655000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S1793830912500474"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012,12]]},"references-count":14,"journal-issue":{"issue":"04","published-online":{"date-parts":[[2013,1,4]]},"published-print":{"date-parts":[[2012,12]]}},"alternative-id":["10.1142\/S1793830912500474"],"URL":"https:\/\/doi.org\/10.1142\/s1793830912500474","relation":{},"ISSN":["1793-8309","1793-8317"],"issn-type":[{"value":"1793-8309","type":"print"},{"value":"1793-8317","type":"electronic"}],"subject":[],"published":{"date-parts":[[2012,12]]}}}