{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,6]],"date-time":"2025-12-06T16:46:06Z","timestamp":1765039566259,"version":"3.37.3"},"reference-count":17,"publisher":"World Scientific Pub Co Pte Ltd","issue":"04","funder":[{"DOI":"10.13039\/501100004541","name":"Ministry of Human Resource Development","doi-asserted-by":"publisher","award":["F. No. 5-6\/2013 -TS-VII dt. 28.09.2015"],"award-info":[{"award-number":["F. No. 5-6\/2013 -TS-VII dt. 28.09.2015"]}],"id":[{"id":"10.13039\/501100004541","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Discrete Math. Algorithm. Appl."],"published-print":{"date-parts":[[2021,8]]},"abstract":"<jats:p> An enormous number of domination parameters have been defined and studied, because of their applications in various fields of science and engineering. From it, we have selected some variation of domination parameters and its generalized form for the study. We have presented a linear programming formulation with linear number of constraints for the selected parameters. MATLAB algorithmic code has been generated to find a minimum dominating set\/function and the domination number of the selected parameters. The domination number and its computational time of five generalized domination parameters, [Formula: see text]-domination, [Formula: see text]-domination, efficient [Formula: see text]-domination, factor domination and [Formula: see text]-domination, have been studied under grid graphs and randomly generated graphs. The computational time for efficient [Formula: see text]-domination and [Formula: see text]-domination numbers is less than [Formula: see text] s, which shows the effectiveness of the formulation. <\/jats:p>","DOI":"10.1142\/s1793830921500440","type":"journal-article","created":{"date-parts":[[2020,11,18]],"date-time":"2020-11-18T03:57:20Z","timestamp":1605671840000},"page":"2150044","source":"Crossref","is-referenced-by-count":4,"title":["Linear programming formulation for some generalized domination parameters"],"prefix":"10.1142","volume":"13","author":[{"given":"Duraisamy","family":"Pandiaraja","sequence":"first","affiliation":[{"name":"National Centre of Excellence, Thiagarajar College, Madurai 625 009, Tamilnadu, India"},{"name":"Department of Mathematics, Thiagarajar College, Madurai 625 009, Tamilnadu, India"}]},{"given":"Esakkimuthu","family":"Shanmugam","sequence":"additional","affiliation":[{"name":"National Centre of Excellence, Thiagarajar College, Madurai 625 009, Tamilnadu, India"}]},{"given":"Rathinakumar","family":"Sivakumar","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Ayya Nadar Janaki Ammal College, Sivakasi 626 124, Tamilnadu, India"}]}],"member":"219","published-online":{"date-parts":[[2020,12,5]]},"reference":[{"key":"S1793830921500440BIB001","unstructured":"C. Berge ,  Theory of Graphs and Its Applications  (Methuen,  London,  1962),  pp. 40\u201351."},{"key":"S1793830921500440BIB002","first-page":"1","author":"Cai Q.","year":"2019","journal-title":"Opt. Methods Softw."},{"key":"S1793830921500440BIB003","doi-asserted-by":"publisher","DOI":"10.1016\/j.dam.2013.06.012"},{"key":"S1793830921500440BIB004","doi-asserted-by":"publisher","DOI":"10.1016\/S0012-365X(02)00522-8"},{"key":"S1793830921500440BIB005","doi-asserted-by":"publisher","DOI":"10.1016\/0167-6377(82)90015-3"},{"key":"S1793830921500440BIB006","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4757-1738-9"},{"issue":"2","key":"S1793830921500440BIB007","first-page":"103","volume":"5","author":"Hedetniemi S. M.","year":"2008","journal-title":"AKCE Int. J. Graphs Combin."},{"key":"S1793830921500440BIB008","doi-asserted-by":"publisher","DOI":"10.1016\/S0167-5060(08)71054-9"},{"key":"S1793830921500440BIB011","doi-asserted-by":"crossref","first-page":"146","DOI":"10.1016\/j.cam.2019.03.006","volume":"358","author":"Ma Y.","year":"2019","journal-title":"Appl. Math. Comput."},{"journal-title":"Discrete Math. Algorithms Appl.","year":"2020","author":"Pandiaraja D.","key":"S1793830921500440BIB012"},{"issue":"2","key":"S1793830921500440BIB013","first-page":"235","volume":"56","author":"Raczek J.","year":"2006","journal-title":"Math. Slovaca."},{"volume-title":"Mathematical Recreations and Problems of Past and Present Times","year":"1892","author":"Rouse Bell W. W.","key":"S1793830921500440BIB014"},{"key":"S1793830921500440BIB015","doi-asserted-by":"publisher","DOI":"10.7151\/dmgt.1371"},{"issue":"5","key":"S1793830921500440BIB016","first-page":"377","volume":"23","author":"Sampathkumar E.","year":"1989","journal-title":"J. Math. Phys. Sci."},{"key":"S1793830921500440BIB017","doi-asserted-by":"publisher","DOI":"10.1145\/321958.321964"},{"volume-title":"Introduction to Graph Theory","year":"2002","author":"West D. B.","key":"S1793830921500440BIB018"},{"key":"S1793830921500440BIB019","doi-asserted-by":"publisher","DOI":"10.1016\/j.dam.2014.05.035"}],"container-title":["Discrete Mathematics, Algorithms and Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S1793830921500440","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,7,12]],"date-time":"2021-07-12T09:04:33Z","timestamp":1626080673000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S1793830921500440"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,12,5]]},"references-count":17,"journal-issue":{"issue":"04","published-print":{"date-parts":[[2021,8]]}},"alternative-id":["10.1142\/S1793830921500440"],"URL":"https:\/\/doi.org\/10.1142\/s1793830921500440","relation":{},"ISSN":["1793-8309","1793-8317"],"issn-type":[{"type":"print","value":"1793-8309"},{"type":"electronic","value":"1793-8317"}],"subject":[],"published":{"date-parts":[[2020,12,5]]}}}