{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,3,30]],"date-time":"2022-03-30T08:47:18Z","timestamp":1648630038562},"reference-count":6,"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":[[2012,3]]},"abstract":"<jats:p> Let k be a positive integer, and let G be a simple graph with vertex set V(G). A function f : V(G) \u2192 {\u00b11, \u00b12, \u2026, \u00b1k} is called a signed total {k}-dominating function if \u2211<jats:sub>u\u2208N(v)<\/jats:sub> f(u) \u2265 k for each vertex v \u2208 V(G). A set {f<jats:sub>1<\/jats:sub>, f<jats:sub>2<\/jats:sub>, \u2026, f<jats:sub>d<\/jats:sub>} of signed total {k}-dominating functions on G with the property that [Formula: see text] for each v\u2208V(G), is called a signed total {k}-dominating family (of functions) on G. The maximum number of functions in a signed total {k}-dominating family on G is the signed total {k}-domatic number of G, denoted by [Formula: see text]. Note that [Formula: see text] is the classical signed total domatic number d<jats:sub>S<\/jats:sub>(G). In this paper, we initiate the study of signed total k-domatic numbers in graphs, and we present some sharp upper bounds for [Formula: see text]. In addition, we determine [Formula: see text] for several classes of graphs. Some of our results are extensions of known properties of the signed total domatic number. <\/jats:p>","DOI":"10.1142\/s1793830912500061","type":"journal-article","created":{"date-parts":[[2012,4,10]],"date-time":"2012-04-10T01:24:02Z","timestamp":1334021042000},"page":"1250006","source":"Crossref","is-referenced-by-count":0,"title":["SIGNED TOTAL {K}-DOMINATION AND {K}-DOMATIC NUMBERS OF GRAPHS"],"prefix":"10.1142","volume":"04","author":[{"given":"S. M.","family":"SHEIKHOLESLAMI","sequence":"first","affiliation":[{"name":"Department of Mathematics, Azarbaijan University of Tarbiat Moallem, Tabriz, Iran"}]},{"given":"L.","family":"VOLKMANN","sequence":"additional","affiliation":[{"name":"Lehrstuhl II fuer Mathematik, RWTH Aachen University, 52056 Aachen, Germany"}]}],"member":"219","published-online":{"date-parts":[[2012,4,13]]},"reference":[{"key":"rf1","doi-asserted-by":"publisher","DOI":"10.1016\/j.disc.2003.06.002"},{"key":"rf2","first-page":"277","volume":"79","author":"Henning M. A.","journal-title":"Ars Combin."},{"key":"rf3","doi-asserted-by":"publisher","DOI":"10.4134\/JKMS.2011.48.3.551"},{"key":"rf4","first-page":"31","volume":"12","author":"Mei G.","journal-title":"J. Shanghai Univ. (Engl. Ed.)"},{"key":"rf5","volume-title":"Introduction to Graph Theory","author":"West D. B.","year":"2000"},{"key":"rf6","doi-asserted-by":"publisher","DOI":"10.1023\/A:1013782511179"}],"container-title":["Discrete Mathematics, Algorithms and Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S1793830912500061","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,7]],"date-time":"2019-08-07T17:53:39Z","timestamp":1565200419000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S1793830912500061"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012,3]]},"references-count":6,"journal-issue":{"issue":"01","published-online":{"date-parts":[[2012,4,13]]},"published-print":{"date-parts":[[2012,3]]}},"alternative-id":["10.1142\/S1793830912500061"],"URL":"https:\/\/doi.org\/10.1142\/s1793830912500061","relation":{},"ISSN":["1793-8309","1793-8317"],"issn-type":[{"value":"1793-8309","type":"print"},{"value":"1793-8317","type":"electronic"}],"subject":[],"published":{"date-parts":[[2012,3]]}}}