{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,25]],"date-time":"2026-03-25T19:26:01Z","timestamp":1774466761092,"version":"3.50.1"},"reference-count":4,"publisher":"World Scientific Pub Co Pte Ltd","issue":"01","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Discrete Math. Algorithm. Appl."],"published-print":{"date-parts":[[2017,2]]},"abstract":"<jats:p> For a connected graph [Formula: see text], a set [Formula: see text] is called a detour dominating set of [Formula: see text], if [Formula: see text] is a detour set and dominating set of [Formula: see text]. The detour domination number [Formula: see text] of [Formula: see text] is the minimum order of its detour dominating sets and any detour dominating set of order [Formula: see text] is called a [Formula: see text] - set of [Formula: see text]. The detour domination numbers of some standard graphs are determined. Connected graph of order [Formula: see text] with detour domination number [Formula: see text] or [Formula: see text] is characterized. For positive integers [Formula: see text] and [Formula: see text] with [Formula: see text], there exists a connected graph with [Formula: see text] and [Formula: see text]. <\/jats:p>","DOI":"10.1142\/s1793830917500069","type":"journal-article","created":{"date-parts":[[2016,10,25]],"date-time":"2016-10-25T03:42:43Z","timestamp":1477366963000},"page":"1750006","source":"Crossref","is-referenced-by-count":9,"title":["The detour domination number of a graph"],"prefix":"10.1142","volume":"09","author":[{"given":"J.","family":"John","sequence":"first","affiliation":[{"name":"Department of Mathematics, Government College of Engineering, Tirunelveli-627007, India"}]},{"given":"N.","family":"Arianayagam","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Government College of Engineering, Tirunelveli-627007, India"}]}],"member":"219","published-online":{"date-parts":[[2017,2,6]]},"reference":[{"key":"S1793830917500069BIB001","volume-title":"Distance in Graphs","author":"Buckley F.","year":"1990"},{"key":"S1793830917500069BIB002","first-page":"75","volume":"53","author":"Chartrand G.","year":"2005","journal-title":"J. Combin. math. combin. comput."},{"key":"S1793830917500069BIB003","first-page":"97","volume":"64","author":"Chartrand G.","year":"2003","journal-title":"Util. math."},{"key":"S1793830917500069BIB004","volume-title":"Fundamentals of Domination in Graphs","author":"Haynes T. W.","year":"1998"}],"container-title":["Discrete Mathematics, Algorithms and Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S1793830917500069","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,6]],"date-time":"2019-08-06T13:04:51Z","timestamp":1565096691000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S1793830917500069"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,2]]},"references-count":4,"journal-issue":{"issue":"01","published-online":{"date-parts":[[2017,2,6]]},"published-print":{"date-parts":[[2017,2]]}},"alternative-id":["10.1142\/S1793830917500069"],"URL":"https:\/\/doi.org\/10.1142\/s1793830917500069","relation":{},"ISSN":["1793-8309","1793-8317"],"issn-type":[{"value":"1793-8309","type":"print"},{"value":"1793-8317","type":"electronic"}],"subject":[],"published":{"date-parts":[[2017,2]]}}}