{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,3,24]],"date-time":"2023-03-24T10:29:44Z","timestamp":1679653784120},"reference-count":5,"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":[[2011,3]]},"abstract":"<jats:p> The closed neighborhood N<jats:sub>G<\/jats:sub>[v] of a vertex v in a graph G is the set consisting of v and of all neighborhood vertices of v. Let f be a function on V(G), the vertex set of G, into the set {-1, 1}. If \u2211<jats:sub>u\u2208N[v]<\/jats:sub> f(u) \u2264 1 for all vertices v of G, then f is called a signed bad function of G. The maximum of the values of \u2211<jats:sub>v\u2208V(G)<\/jats:sub> f(v), taking the maximum over all signed bad functions f of G, is called the signed bad number of G and denoted by \u03b2<jats:sub> s <\/jats:sub>(G). In this paper, we establish some upper bounds on the signed bad numbers for general graphs. In addition, we determine \u03b2<jats:sub> s <\/jats:sub>(G), when G is a complete graph, a cycle or a path. <\/jats:p>","DOI":"10.1142\/s1793830911000997","type":"journal-article","created":{"date-parts":[[2011,4,14]],"date-time":"2011-04-14T09:45:47Z","timestamp":1302774347000},"page":"33-41","source":"Crossref","is-referenced-by-count":4,"title":["THE SIGNED BAD NUMBERS IN GRAPHS"],"prefix":"10.1142","volume":"03","author":[{"given":"A. N.","family":"GHAMESHLOU","sequence":"first","affiliation":[{"name":"Department of Mathematics, University of Mazandaran, Babolsar, Iran"}]},{"given":"ABDOLLAH","family":"KHODKAR","sequence":"additional","affiliation":[{"name":"Department of Mathematics, University of West Georgia, Carrollton, GA 30118, USA"}]},{"given":"S. M.","family":"SHEIKHOLESLAMI","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Azarbaijan University of Tarbiat Moallem, Tabriz, Iran"}]}],"member":"219","published-online":{"date-parts":[[2012,4,5]]},"reference":[{"key":"rf1","unstructured":"J.\u00a0Dunbar, Signed Domination in Graphs, Graph Theory, Combinatorics, and Application\u00a01 (Wiley, New York, 1995)\u00a0pp. 311\u2013322."},{"key":"rf2","doi-asserted-by":"publisher","DOI":"10.1016\/0012-365X(96)00026-X"},{"key":"rf3","volume-title":"Domination in Graphs: Advance Topics","author":"Haynes T. W.","year":"1998"},{"key":"rf4","first-page":"263","volume":"41","author":"Wang C. P.","journal-title":"Australas. J. Combin."},{"key":"rf5","volume-title":"Introduction to Graph Theory","author":"West D. B.","year":"2000"}],"container-title":["Discrete Mathematics, Algorithms and Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S1793830911000997","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,7]],"date-time":"2019-08-07T01:32:19Z","timestamp":1565141539000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S1793830911000997"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2011,3]]},"references-count":5,"journal-issue":{"issue":"01","published-online":{"date-parts":[[2012,4,5]]},"published-print":{"date-parts":[[2011,3]]}},"alternative-id":["10.1142\/S1793830911000997"],"URL":"https:\/\/doi.org\/10.1142\/s1793830911000997","relation":{},"ISSN":["1793-8309","1793-8317"],"issn-type":[{"value":"1793-8309","type":"print"},{"value":"1793-8317","type":"electronic"}],"subject":[],"published":{"date-parts":[[2011,3]]}}}