{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T16:39:12Z","timestamp":1740155952590,"version":"3.37.3"},"reference-count":16,"publisher":"World Scientific Pub Co Pte Ltd","issue":"06","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Discrete Math. Algorithm. Appl."],"published-print":{"date-parts":[[2019,12]]},"abstract":"<jats:p> A dominator coloring (respectively, total dominator coloring) of a graph [Formula: see text] is a proper coloring [Formula: see text] of [Formula: see text] such that each closed neighborhood (respectively, open neighborhood) of every vertex of [Formula: see text] contains a color class of [Formula: see text] The minimum number of colors required for a dominator coloring (respectively, total dominator coloring) of [Formula: see text] is called the dominator chromatic number (respectively, total dominator chromatic number) of [Formula: see text] and is denoted by [Formula: see text] (respectively, [Formula: see text]). In this paper, we prove that the dominator coloring problem and the total dominator coloring problem are solvable in linear time for trestled graphs. <\/jats:p>","DOI":"10.1142\/s1793830919500666","type":"journal-article","created":{"date-parts":[[2019,9,18]],"date-time":"2019-09-18T04:27:31Z","timestamp":1568780851000},"page":"1950066","source":"Crossref","is-referenced-by-count":0,"title":["Linear time algorithm for dominator chromatic number of trestled graphs"],"prefix":"10.1142","volume":"11","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-4477-9453","authenticated-orcid":false,"given":"S.","family":"Arumugam","sequence":"first","affiliation":[{"name":"National Centre for Advanced Research in Discrete Mathematics (-CARDMATH), Kalasalingam Academy of Research and Education, Anand Nagar, Krishnankoil 626126, Tamil Nadu, India"}]},{"given":"K.","family":"Raja Chandrasekar","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Amrita College of Engineering and Technology, Amritagiri, Erachakulam Post, Nagercoil 629902, Tamil Nadu, India"}]}],"member":"219","published-online":{"date-parts":[[2019,12,19]]},"reference":[{"key":"S1793830919500666BIB001","doi-asserted-by":"publisher","DOI":"10.1016\/j.disc.2007.12.057"},{"key":"S1793830919500666BIB002","doi-asserted-by":"publisher","DOI":"10.1007\/s12044-012-0092-5"},{"key":"S1793830919500666BIB003","first-page":"449","volume-title":"Handbook of Graph Theory, Combinatorial Optimization, and Algorithms","author":"Arumugam S.","year":"2016"},{"key":"S1793830919500666BIB004","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-25011-8_2"},{"key":"S1793830919500666BIB005","doi-asserted-by":"publisher","DOI":"10.1142\/S1793830910000589"},{"key":"S1793830919500666BIB006","volume-title":"Graphs and Digraphs","author":"Chartrand G.","year":"2005","edition":"4"},{"key":"S1793830919500666BIB007","doi-asserted-by":"publisher","DOI":"10.1007\/s00373-010-1012-z"},{"key":"S1793830919500666BIB008","doi-asserted-by":"publisher","DOI":"10.1007\/s00373-016-1742-7"},{"key":"S1793830919500666BIB009","doi-asserted-by":"publisher","DOI":"10.1137\/S0895480191199026"},{"key":"S1793830919500666BIB010","first-page":"25","volume-title":"Graph Theory Notes","author":"Gera R. 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Raja Chandrasekar,  Dominator Colorings of Products of Graphs,  Lecture Notes in Computer Science, Vol.  10398  (Springer, 2017),  pp. 1\u20139."}],"container-title":["Discrete Mathematics, Algorithms and Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S1793830919500666","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,12,20]],"date-time":"2019-12-20T01:43:19Z","timestamp":1576806199000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S1793830919500666"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,12]]},"references-count":16,"journal-issue":{"issue":"06","published-print":{"date-parts":[[2019,12]]}},"alternative-id":["10.1142\/S1793830919500666"],"URL":"https:\/\/doi.org\/10.1142\/s1793830919500666","relation":{},"ISSN":["1793-8309","1793-8317"],"issn-type":[{"type":"print","value":"1793-8309"},{"type":"electronic","value":"1793-8317"}],"subject":[],"published":{"date-parts":[[2019,12]]}}}