{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,3]],"date-time":"2022-04-03T16:59:25Z","timestamp":1649005165653},"reference-count":9,"publisher":"World Scientific Pub Co Pte Lt","issue":"01","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Discrete Math. Algorithm. Appl."],"published-print":{"date-parts":[[2019,2]]},"abstract":"<jats:p>In [S. M. Hegde, Set colorings of graphs, European J. Combin. 30 (2009) 986\u2013995.] Hegde introduced the notion of set colorings of a graph [Formula: see text] as an assignment of distinct subsets of a finite set [Formula: see text] of [Formula: see text] colors to the vertices of [Formula: see text] such that all the colors of the edges which are obtained as the symmetric differences of the subsets assigned to their end-vertices are distinct. Additionally, if all the sets on the vertices and edges of [Formula: see text] are the set of all nonempty subsets of [Formula: see text] then the coloring is said to be a strong set-coloring and [Formula: see text] is said to be strongly set-colorable. In this paper, we report some new necessary conditions and propose a conjuncture for the sufficient condition for a graph to admit strong set-coloring. We also identify and characterize some new classes of graphs admitting strong set-coloring. In addition to these, we also propose strategies to construct infinite families graphs admitting strong set-coloring.<\/jats:p>","DOI":"10.1142\/s1793830919500071","type":"journal-article","created":{"date-parts":[[2018,11,16]],"date-time":"2018-11-16T06:19:11Z","timestamp":1542349151000},"page":"1950007","source":"Crossref","is-referenced-by-count":0,"title":["Strongly set-colorable graphs"],"prefix":"10.1142","volume":"11","author":[{"given":"Kumar","family":"Abhishek","sequence":"first","affiliation":[{"name":"Department of Mathematics, Amrita School of Engineering, Amrita Vishwa Vidyapeetham, Coimbatore-641112, India"}]}],"member":"219","published-online":{"date-parts":[[2019,2,8]]},"reference":[{"key":"S1793830919500071BIB001","series-title":"MRI Lecture Notes in Applied Mathematics","volume-title":"Set-Valuations and Their Applications","volume":"2","author":"Acharya B. D.","year":"1983"},{"key":"S1793830919500071BIB002","doi-asserted-by":"crossref","first-page":"#R173","DOI":"10.37236\/445","volume":"17","author":"Boutin J. P.","year":"2010","journal-title":"The Electronic Journal of Combinatorics"},{"key":"S1793830919500071BIB003","doi-asserted-by":"publisher","DOI":"10.1002\/jgt.10076"},{"key":"S1793830919500071BIB004","volume-title":"Graphs and Hypergraphs","author":"Berge C.","year":"1973"},{"key":"S1793830919500071BIB005","first-page":"241","volume":"14","author":"Frank O.","year":"1982","journal-title":"Ars Combin."},{"key":"S1793830919500071BIB006","doi-asserted-by":"publisher","DOI":"10.21236\/AD0705364"},{"key":"S1793830919500071BIB007","doi-asserted-by":"publisher","DOI":"10.1016\/j.ejc.2008.06.005"},{"key":"S1793830919500071BIB008","doi-asserted-by":"publisher","DOI":"10.1137\/0604032"},{"key":"S1793830919500071BIB009","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\/S1793830919500071","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,11,15]],"date-time":"2020-11-15T10:10:17Z","timestamp":1605435017000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S1793830919500071"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,2]]},"references-count":9,"journal-issue":{"issue":"01","published-online":{"date-parts":[[2019,2,8]]},"published-print":{"date-parts":[[2019,2]]}},"alternative-id":["10.1142\/S1793830919500071"],"URL":"https:\/\/doi.org\/10.1142\/s1793830919500071","relation":{},"ISSN":["1793-8309","1793-8317"],"issn-type":[{"value":"1793-8309","type":"print"},{"value":"1793-8317","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,2]]}}}