{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,4]],"date-time":"2022-04-04T04:37:12Z","timestamp":1649047032542},"reference-count":12,"publisher":"World Scientific Pub Co Pte Lt","issue":"02","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Discrete Math. Algorithm. Appl."],"published-print":{"date-parts":[[2015,6]]},"abstract":"<jats:p> Let D be a simple digraph with arc set A(D), and let j and k be two positive integers. A function f : A(D) \u2192 {-1, 1} is said to be a signed star j-dominating function (SSjDF) on D if \u2211<jats:sub>a \u2208 A(v)<\/jats:sub> f(a) \u2265 j for every vertex v of D, where A(v) is the set of arcs with head v. A set {f<jats:sub>1<\/jats:sub>, f<jats:sub>2<\/jats:sub>, \u2026, f<jats:sub>d<\/jats:sub>} of distinct SSjDFs on D with the property that [Formula: see text] for each a \u2208 A(D), is called a signed star (j, k)-dominating (SS(j, k)D) family (of functions) on D. The maximum number of functions in a SS(j, k)D family on D is the signed star (j, k)-domatic number of D, denoted by [Formula: see text]. In this paper, we study properties of the signed star (j, k)-domatic number of a digraph D. In particular, we determine bounds on [Formula: see text]. Some of our results extend these ones given by Sheikholeslami and Volkmann [Signed star k-domination and k-domatic number of digraphs, submitted] for the signed (j, 1)-domatic number. <\/jats:p>","DOI":"10.1142\/s1793830915500068","type":"journal-article","created":{"date-parts":[[2015,1,21]],"date-time":"2015-01-21T03:18:26Z","timestamp":1421810306000},"page":"1550006","source":"Crossref","is-referenced-by-count":0,"title":["Signed star (j, k)-domatic numbers of digraphs"],"prefix":"10.1142","volume":"07","author":[{"given":"S. M.","family":"Sheikholeslami","sequence":"first","affiliation":[{"name":"Department of Mathematics, Azarbaijan Shahid Madani University, Tabriz, Iran"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"L.","family":"Volkmann","sequence":"additional","affiliation":[{"name":"Lehrstuhl II f\u00fcr Mathematik, RWTH-Aachen University, 52056 Aachen, Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2015,5,25]]},"reference":[{"key":"rf1","doi-asserted-by":"publisher","DOI":"10.1016\/j.dam.2009.09.015"},{"key":"rf2","doi-asserted-by":"publisher","DOI":"10.1142\/S1793830912500176"},{"key":"rf3","volume-title":"Fundamentals of Domination in Graphs","author":"Haynes T. W.","year":"1998"},{"key":"rf4","doi-asserted-by":"publisher","DOI":"10.1016\/j.dam.2008.01.020"},{"key":"rf5","first-page":"20","volume":"6","author":"Sheikholeslami S. M.","year":"2011","journal-title":"Contrib. Discrete Math."},{"key":"rf6","first-page":"19","volume":"83","author":"Sheikholeslami S. M.","year":"2014","journal-title":"Acta Math. Univ. Comenian."},{"key":"rf7","doi-asserted-by":"publisher","DOI":"10.7494\/OpMath.2014.34.3.609"},{"key":"rf9","doi-asserted-by":"publisher","DOI":"10.1016\/j.dam.2007.04.008"},{"key":"rf10","first-page":"1","volume":"5","author":"Wang C. P.","year":"2010","journal-title":"Contrib. Discrete Math."},{"key":"rf11","doi-asserted-by":"publisher","DOI":"10.1016\/j.disc.2004.11.008"},{"key":"rf12","doi-asserted-by":"publisher","DOI":"10.1016\/j.dam.2005.12.007"},{"key":"rf13","first-page":"638","volume":"25","author":"Xu B.","year":"2009","journal-title":"Pure Appl. Math. (Xi'an)"}],"container-title":["Discrete Mathematics, Algorithms and Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S1793830915500068","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,7]],"date-time":"2019-08-07T03:35:45Z","timestamp":1565148945000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S1793830915500068"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,5,25]]},"references-count":12,"journal-issue":{"issue":"02","published-online":{"date-parts":[[2015,5,25]]},"published-print":{"date-parts":[[2015,6]]}},"alternative-id":["10.1142\/S1793830915500068"],"URL":"https:\/\/doi.org\/10.1142\/s1793830915500068","relation":{},"ISSN":["1793-8309","1793-8317"],"issn-type":[{"value":"1793-8309","type":"print"},{"value":"1793-8317","type":"electronic"}],"subject":[],"published":{"date-parts":[[2015,5,25]]}}}