{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T14:34:55Z","timestamp":1753886095729,"version":"3.41.2"},"reference-count":3,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2011,2,24]],"date-time":"2011-02-24T00:00:00Z","timestamp":1298505600000},"content-version":"vor","delay-in-days":54,"URL":"http:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["International Journal of Mathematics and Mathematical Sciences"],"published-print":{"date-parts":[[2011,1]]},"abstract":"<jats:p>A mapping <jats:italic>x<\/jats:italic> : <jats:italic>V<\/jats:italic> \u2192 {\u22121,1} is called <jats:italic>negative<\/jats:italic> if \u2211<jats:sub><jats:italic>u<\/jats:italic>\u2208<jats:italic>N<\/jats:italic>[<jats:italic>v<\/jats:italic>]<\/jats:sub><jats:italic>x<\/jats:italic>(<jats:italic>u<\/jats:italic>) \u2264 1 for every <jats:italic>v<\/jats:italic> \u2208 <jats:italic>V<\/jats:italic>. The maximum of the values of \u2211<jats:sub><jats:italic>v<\/jats:italic>\u2208<jats:italic>V<\/jats:italic><\/jats:sub><jats:italic>x<\/jats:italic>(<jats:italic>v<\/jats:italic>) taken over all negative mappings <jats:italic>x<\/jats:italic>, is called the <jats:italic>modified negative decision number<\/jats:italic> and is denoted by <jats:italic>\u03b2<\/jats:italic><jats:sub><jats:italic>D<\/jats:italic><\/jats:sub>\u2009<jats:sup>\u2032<\/jats:sup>(<jats:italic>G<\/jats:italic>). In this paper, several sharp upper bounds of this number for a general graph are presented. Exact values of these numbers for cycles, paths, cliques and bicliques are found.<\/jats:p>","DOI":"10.1155\/2011\/135481","type":"journal-article","created":{"date-parts":[[2011,2,24]],"date-time":"2011-02-24T19:32:07Z","timestamp":1298575927000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["The Modified Negative Decision Number in Graphs"],"prefix":"10.1155","volume":"2011","author":[{"given":"Changping","family":"Wang","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2011,2,24]]},"reference":[{"key":"e_1_2_3_1_2","first-page":"263","article-title":"The negative decision number in graphs","volume":"41","author":"Wang C.","year":"2008","journal-title":"The Australasian Journal of Combinatorics"},{"volume-title":"Graphs & Digraphs","year":"2000","author":"Chartrand G.","key":"e_1_2_3_2_2"},{"volume-title":"Introduction to Graph Theory","year":"2001","author":"West D. B.","key":"e_1_2_3_3_2"}],"container-title":["International Journal of Mathematics and Mathematical Sciences"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/ijmms\/2011\/135481.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/ijmms\/2011\/135481.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1155\/2011\/135481","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,6,10]],"date-time":"2024-06-10T13:43:33Z","timestamp":1718027013000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1155\/2011\/135481"}},"subtitle":[],"editor":[{"given":"Dalibor","family":"Froncek","sequence":"additional","affiliation":[],"role":[{"role":"editor","vocabulary":"crossref"}]}],"short-title":[],"issued":{"date-parts":[[2011,1]]},"references-count":3,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2011,1]]}},"alternative-id":["10.1155\/2011\/135481"],"URL":"https:\/\/doi.org\/10.1155\/2011\/135481","archive":["Portico"],"relation":{},"ISSN":["0161-1712","1687-0425"],"issn-type":[{"type":"print","value":"0161-1712"},{"type":"electronic","value":"1687-0425"}],"subject":[],"published":{"date-parts":[[2011,1]]},"assertion":[{"value":"2010-12-14","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2011-01-11","order":1,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2011-02-24","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}],"article-number":"135481"}}