{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T14:22:11Z","timestamp":1753885331695,"version":"3.41.2"},"reference-count":10,"publisher":"World Scientific Pub Co Pte Ltd","issue":"06","funder":[{"DOI":"10.13039\/501100003725","name":"the National Research Foundation of Korea","doi-asserted-by":"crossref","award":["2020R1I1A1A01055403"],"award-info":[{"award-number":["2020R1I1A1A01055403"]}],"id":[{"id":"10.13039\/501100003725","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Discrete Math. Algorithm. Appl."],"published-print":{"date-parts":[[2021,12]]},"abstract":"<jats:p> Let [Formula: see text] be a finite simple graph. The middle graph [Formula: see text] of a graph [Formula: see text] is the graph obtained by subdividing each edge of [Formula: see text] exactly once and joining all these newly introduced vertices of adjacent edges of [Formula: see text]. The middle domination number [Formula: see text] of [Formula: see text] is defined by the domination number [Formula: see text] of the middle graph [Formula: see text]. A subset [Formula: see text] of [Formula: see text] is a 2-independent set of [Formula: see text] if every vertex of [Formula: see text] has at most one neighbor in [Formula: see text]. The maximum cardinality of a 2-independent set of [Formula: see text] is the 2-independence number [Formula: see text]. These parameters are incomparable in general. However, we show that [Formula: see text] for any tree [Formula: see text]. We also characterize all trees attaining the equality. <\/jats:p>","DOI":"10.1142\/s1793830921500798","type":"journal-article","created":{"date-parts":[[2020,12,23]],"date-time":"2020-12-23T03:58:12Z","timestamp":1608695892000},"source":"Crossref","is-referenced-by-count":2,"title":["Middle domination and 2-independence in trees"],"prefix":"10.1142","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-6623-5123","authenticated-orcid":false,"given":"Kijung","family":"Kim","sequence":"first","affiliation":[{"name":"Department of Mathematics, Pusan National University, Busandaehak-ro 63beon-gil, Geumjeong-gu, Busan 46241, Republic of Korea"}]}],"member":"219","published-online":{"date-parts":[[2021,1,21]]},"reference":[{"key":"S1793830921500798BIB001","series-title":"Graduate Texts in Mathematics","volume-title":"Graph Theory","volume":"244","author":"Bondy J. A.","year":"2007"},{"key":"S1793830921500798BIB002","first-page":"317","volume":"33","author":"Blidia M.","year":"2005","journal-title":"Australas. J. Combin."},{"doi-asserted-by":"publisher","key":"S1793830921500798BIB003","DOI":"10.7151\/dmgt.1603"},{"key":"S1793830921500798BIB004","first-page":"79","volume":"3","author":"Dehgardi N.","year":"2018","journal-title":"Commun. Comb. Optim."},{"doi-asserted-by":"publisher","key":"S1793830921500798BIB005","DOI":"10.1016\/0095-8956(85)90040-1"},{"key":"S1793830921500798BIB006","first-page":"301","volume-title":"Graph Theory with Applications to Algorithms and Computer Science","author":"Fink J. F.","year":"1985"},{"doi-asserted-by":"publisher","key":"S1793830921500798BIB007","DOI":"10.1016\/0012-365X(76)90037-6"},{"key":"S1793830921500798BIB008","first-page":"151","volume":"29","author":"Jacobson M. S.","year":"1990","journal-title":"Ars Combin."},{"doi-asserted-by":"publisher","key":"S1793830921500798BIB010","DOI":"10.1142\/S1793830917500239"},{"doi-asserted-by":"publisher","key":"S1793830921500798BIB011","DOI":"10.3934\/math.2020357"}],"container-title":["Discrete Mathematics, Algorithms and Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S1793830921500798","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,12,8]],"date-time":"2021-12-08T11:33:09Z","timestamp":1638963189000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S1793830921500798"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,1,21]]},"references-count":10,"journal-issue":{"issue":"06","published-print":{"date-parts":[[2021,12]]}},"alternative-id":["10.1142\/S1793830921500798"],"URL":"https:\/\/doi.org\/10.1142\/s1793830921500798","relation":{},"ISSN":["1793-8309","1793-8317"],"issn-type":[{"type":"print","value":"1793-8309"},{"type":"electronic","value":"1793-8317"}],"subject":[],"published":{"date-parts":[[2021,1,21]]},"article-number":"2150079"}}