{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T14:16:13Z","timestamp":1753884973405,"version":"3.41.2"},"reference-count":7,"publisher":"World Scientific Pub Co Pte Ltd","issue":"08","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Discrete Math. Algorithm. Appl."],"published-print":{"date-parts":[[2023,11]]},"abstract":"<jats:p> In this paper, we give a class of graphs that do not admit disjoint maximum and maximal independent (MMI) sets. The concept of inverse independence was introduced by Bhat and Bhat in [Inverse independence number of a graph, Int. J. Comput. Appl.\u00a042(5) (2012) 9\u201313]. Let [Formula: see text] be a [Formula: see text]-set in [Formula: see text]. An independent set [Formula: see text] is called an inverse independent set with respect to [Formula: see text]. The inverse independence number [Formula: see text] is the size of the largest inverse independent set in [Formula: see text]. Bhat and Bhat gave few bounds on the independence number of a graph, we continue the study by giving some new bounds and exact value for particular classes of graphs: spider tree, the rooted product and Cartesian product of two particular graphs. <\/jats:p>","DOI":"10.1142\/s1793830922501658","type":"journal-article","created":{"date-parts":[[2022,9,25]],"date-time":"2022-09-25T14:14:23Z","timestamp":1664115263000},"source":"Crossref","is-referenced-by-count":0,"title":["On disjoint maximum and maximal independent sets in graphs and inverse independence number"],"prefix":"10.1142","volume":"15","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-5019-7663","authenticated-orcid":false,"given":"Fatma","family":"Kaci","sequence":"first","affiliation":[{"name":"Department of Mathematics, University of Mohamed Khider, B.P 145, Biskra, Algeria"}]}],"member":"219","published-online":{"date-parts":[[2022,10,28]]},"reference":[{"key":"S1793830922501658BIB001","doi-asserted-by":"crossref","first-page":"25","DOI":"10.7151\/dmgt.1527","volume":"31","author":"Abay-Asmerom G.","year":"2011","journal-title":"Discuss. Math. Graph Theory"},{"issue":"5","key":"S1793830922501658BIB002","first-page":"9","volume":"42","author":"Bhat P. G.","year":"2012","journal-title":"Int. J. Comput. Appl."},{"key":"S1793830922501658BIB003","first-page":"149","volume":"43","author":"Hagauer J.","year":"1996","journal-title":"Ars Comb."},{"key":"S1793830922501658BIB004","first-page":"173","volume":"74","author":"Klav\u017ear S.","year":"2005","journal-title":"Ars Comb."},{"key":"S1793830922501658BIB005","doi-asserted-by":"crossref","first-page":"199","DOI":"10.1007\/s40840-015-0182-5","volume":"39","author":"Kuziak D.","year":"2016","journal-title":"Bull. Malays. Math. Sci. Soc."},{"issue":"1","key":"S1793830922501658BIB006","doi-asserted-by":"crossref","first-page":"23","DOI":"10.1016\/j.ipl.2014.08.010","volume":"155","author":"Schaudt O.","year":"2015","journal-title":"Inf. Process. Lett."},{"key":"S1793830922501658BIB007","first-page":"30","volume":"9","author":"Vizing V. G.","year":"1963","journal-title":"Vych. Sys."}],"container-title":["Discrete Mathematics, Algorithms and Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S1793830922501658","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,8,15]],"date-time":"2023-08-15T02:53:24Z","timestamp":1692068004000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/10.1142\/S1793830922501658"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,10,28]]},"references-count":7,"journal-issue":{"issue":"08","published-print":{"date-parts":[[2023,11]]}},"alternative-id":["10.1142\/S1793830922501658"],"URL":"https:\/\/doi.org\/10.1142\/s1793830922501658","relation":{},"ISSN":["1793-8309","1793-8317"],"issn-type":[{"type":"print","value":"1793-8309"},{"type":"electronic","value":"1793-8317"}],"subject":[],"published":{"date-parts":[[2022,10,28]]},"article-number":"2250165"}}