{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,25]],"date-time":"2025-11-25T20:39:11Z","timestamp":1764103151676},"reference-count":13,"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":[[2021,4]]},"abstract":"<jats:p> Let [Formula: see text] be a finite graph, simple, undirected and has no isolated vertex. A dominating subset [Formula: see text] of [Formula: see text] is said a bi-dominating set, if every vertex of it dominates two vertices of [Formula: see text]. The bi-domination number of [Formula: see text], denoted by [Formula: see text] is the minimum cardinality over all bi-dominating sets in [Formula: see text]. In this paper, a certain modified bi-domination parameter called doubly connected bi-domination and its inverse are introduced. Several bounds and properties are studied here. These modified dominations are applied and evaluated for several well-known graphs and complement graphs. <\/jats:p>","DOI":"10.1142\/s1793830921500099","type":"journal-article","created":{"date-parts":[[2020,8,16]],"date-time":"2020-08-16T10:14:49Z","timestamp":1597572889000},"page":"2150009","source":"Crossref","is-referenced-by-count":13,"title":["Doubly connected bi-domination in graphs"],"prefix":"10.1142","volume":"13","author":[{"given":"Mohammed A.","family":"Abdlhusein","sequence":"first","affiliation":[{"name":"Department of Mathematics, College of Education for Pure Sciences, Thi-Qar University, Thi-Qar, Iraq"}]}],"member":"219","published-online":{"date-parts":[[2020,9,19]]},"reference":[{"key":"S1793830921500099BIB001","author":"Abdlhusein M. A.","year":"2020","journal-title":"Indian J. Pure Appl. Math."},{"key":"S1793830921500099BIB002","doi-asserted-by":"publisher","DOI":"10.1142\/S1793830920500251"},{"issue":"1","key":"S1793830921500099BIB003","doi-asserted-by":"crossref","first-page":"020013","DOI":"10.1063\/1.5097810","volume":"2096","author":"Al-Harere M. N.","year":"2019","journal-title":"AIP Conf. Proc."},{"key":"S1793830921500099BIB004","doi-asserted-by":"crossref","first-page":"2885","DOI":"10.1016\/j.dam.2013.06.012","volume":"18","author":"Chellali M.","year":"2013","journal-title":"Disc. Appl. Math."},{"issue":"1","key":"S1793830921500099BIB005","first-page":"34","volume":"4","author":"Cyman J.","year":"2006","journal-title":"Central European J. Math."},{"key":"S1793830921500099BIB006","doi-asserted-by":"crossref","first-page":"193","DOI":"10.1007\/s00373-017-1869-1","volume":"1","author":"Das A.","year":"2018","journal-title":"Graphs Comb."},{"key":"S1793830921500099BIB007","doi-asserted-by":"crossref","DOI":"10.21236\/AD0705364","volume-title":"Graph Theory","author":"Harary F.","year":"1969"},{"key":"S1793830921500099BIB008","volume-title":"Domination in Graphs-Advanced Topics","author":"Haynes T. W.","year":"1998"},{"key":"S1793830921500099BIB009","series-title":"Discrete Mathematics","volume-title":"Topics in Domination in Graphs","volume":"86","author":"Hedetneimi S. T.","year":"1990"},{"issue":"12","key":"S1793830921500099BIB010","first-page":"14165","volume":"119","author":"Natarajan C.","year":"2018","journal-title":"Int. J. Pure App. Math."},{"key":"S1793830921500099BIB011","first-page":"242","volume":"1","author":"Omran A. A.","year":"2019","journal-title":"Baghdad Sci. J."},{"key":"S1793830921500099BIB012","doi-asserted-by":"crossref","DOI":"10.1090\/coll\/038","volume-title":"Theory of Graphs","author":"Ore O.","year":"1962"},{"key":"S1793830921500099BIB013","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-319-49475-3","volume-title":"Basic Graph Theory","author":"Rahman M. S.","year":"2017"}],"container-title":["Discrete Mathematics, Algorithms and Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S1793830921500099","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,2,8]],"date-time":"2021-02-08T16:55:50Z","timestamp":1612803350000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S1793830921500099"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,9,19]]},"references-count":13,"journal-issue":{"issue":"02","published-print":{"date-parts":[[2021,4]]}},"alternative-id":["10.1142\/S1793830921500099"],"URL":"https:\/\/doi.org\/10.1142\/s1793830921500099","relation":{},"ISSN":["1793-8309","1793-8317"],"issn-type":[{"value":"1793-8309","type":"print"},{"value":"1793-8317","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,9,19]]}}}