{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T14:21:56Z","timestamp":1753885316523,"version":"3.41.2"},"reference-count":7,"publisher":"World Scientific Pub Co Pte Ltd","issue":"03","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Discrete Math. Algorithm. Appl."],"published-print":{"date-parts":[[2023,4]]},"abstract":"<jats:p> Let [Formula: see text] be a non-empty, finite graph. If the vertices of G can be bijectively labeled by a set S of positive distinct real numbers with two vertices being adjacent if and only if the positive difference of the corresponding labels is in S, then G is called a proper monograph. The set S is called the signature of G and denoted as G(S). Not all proper monographs have the property that a set of idle vertices can be bijectively mapped to the maximum independent sets. As a result, in this paper, we present the proper monograph labelings of several classes of graphs that satisfy the property mentioned above. We present the proper monograph labelings of graphs such as cycles, [Formula: see text], cycles with paths attached to one or more vertices, and Cycles with an irreducible tree attached to one or more vertices. <\/jats:p>","DOI":"10.1142\/s1793830922500926","type":"journal-article","created":{"date-parts":[[2022,4,19]],"date-time":"2022-04-19T15:08:03Z","timestamp":1650380883000},"source":"Crossref","is-referenced-by-count":0,"title":["Maximum independent sets in a proper monograph determined through a signature"],"prefix":"10.1142","volume":"15","author":[{"given":"S. M.","family":"Hegde","sequence":"first","affiliation":[{"name":"Department of Mathematical and Computational Sciences, National Institute of Technology Karnataka, Surathkal 575025, India"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6755-7880","authenticated-orcid":false,"given":"Y. M.","family":"Saumya","sequence":"additional","affiliation":[{"name":"Department of Mathematical and Computational Sciences, National Institute of Technology Karnataka, Surathkal 575025, India"}]}],"member":"219","published-online":{"date-parts":[[2022,5,5]]},"reference":[{"issue":"1","key":"S1793830922500926BIB001","doi-asserted-by":"crossref","first-page":"93","DOI":"10.1111\/j.1749-6632.1979.tb32778.x","volume":"319","author":"Bloom G. S.","year":"1979","journal-title":"Ann. New York Acad. Sci."},{"key":"S1793830922500926BIB002","first-page":"64","volume":"59","author":"Fontanil L. L.","year":"2014","journal-title":"Aust. J. Comb."},{"key":"S1793830922500926BIB003","first-page":"1","volume":"6","author":"Gervacio S. V.","year":"1982","journal-title":"Matimyas Mat."},{"issue":"1","key":"S1793830922500926BIB004","first-page":"79","volume":"6","author":"Hegde S. M.","year":"2009","journal-title":"AKCE Int. J. Graphs Combin."},{"issue":"1","key":"S1793830922500926BIB005","doi-asserted-by":"crossref","first-page":"55","DOI":"10.7151\/dmgt.1185","volume":"23","author":"Sonntag M.","year":"2003","journal-title":"Discuss. Math. Graph Theory"},{"issue":"3","key":"S1793830922500926BIB006","doi-asserted-by":"crossref","first-page":"509","DOI":"10.7151\/dmgt.1249","volume":"24","author":"Sonntag M.","year":"2004","journal-title":"Discuss. Math. Graph Theory"},{"key":"S1793830922500926BIB007","first-page":"277","volume":"37","author":"Sugeng K. A.","year":"2007","journal-title":"Aust. J. Combin."}],"container-title":["Discrete Mathematics, Algorithms and Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S1793830922500926","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,3,24]],"date-time":"2023-03-24T10:12:57Z","timestamp":1679652777000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/10.1142\/S1793830922500926"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,5,5]]},"references-count":7,"journal-issue":{"issue":"03","published-print":{"date-parts":[[2023,4]]}},"alternative-id":["10.1142\/S1793830922500926"],"URL":"https:\/\/doi.org\/10.1142\/s1793830922500926","relation":{},"ISSN":["1793-8309","1793-8317"],"issn-type":[{"type":"print","value":"1793-8309"},{"type":"electronic","value":"1793-8317"}],"subject":[],"published":{"date-parts":[[2022,5,5]]},"article-number":"2250092"}}