{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T14:17:01Z","timestamp":1753885021459,"version":"3.41.2"},"reference-count":7,"publisher":"World Scientific Pub Co Pte Ltd","issue":"01","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Discrete Math. Algorithm. Appl."],"published-print":{"date-parts":[[2025,1]]},"abstract":"<jats:p> A bijective product square [Formula: see text]-cordial labeling of a graph [Formula: see text] with vertex set [Formula: see text] and edge set [Formula: see text] is a bijection [Formula: see text] from [Formula: see text] to [Formula: see text] such that the induced edge function [Formula: see text] from [Formula: see text] to [Formula: see text] defined as [Formula: see text] for every edge [Formula: see text] satisfies the following condition. (i) If [Formula: see text] is the number of edges labeled with [Formula: see text] under [Formula: see text], then [Formula: see text] where [Formula: see text]. A graph which admits a bijective product square [Formula: see text]-cordial labeling is called bijective product square [Formula: see text]-cordial graph. In this paper, we find upper limit of the size of the bijective product square [Formula: see text]-cordial graph for [Formula: see text] and [Formula: see text]. Also, we prove that every graph is a subgraph of a connected bijective product square [Formula: see text]-cordial graph for all odd prime [Formula: see text]. In addition, we establish the relation between bijective product square [Formula: see text]-cordial and [Formula: see text]-product cordial graphs. <\/jats:p>","DOI":"10.1142\/s1793830924500137","type":"journal-article","created":{"date-parts":[[2024,1,27]],"date-time":"2024-01-27T03:47:45Z","timestamp":1706327265000},"source":"Crossref","is-referenced-by-count":0,"title":["On bijective product square k-cordial labeling"],"prefix":"10.1142","volume":"17","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-7510-2798","authenticated-orcid":false,"given":"R.","family":"Santrin Sabibha","sequence":"first","affiliation":[{"name":"Research Centre, Department of Mathematics, Govindammal Aditanar College for Women, Tiruchendur-628215, Tamilnadu, India"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4477-7324","authenticated-orcid":false,"given":"K.","family":"Jeya Daisy","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Holy Cross College, Nagercoil 629004, Tamilnadu, India"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4349-164X","authenticated-orcid":false,"given":"P.","family":"Jeyanthi","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Govindammal Aditanar College for Women, Tiruchendur 628215, Tamilnadu, India"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0365-1891","authenticated-orcid":false,"given":"Maged Z.","family":"Youssef","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Statistics, College of Science, Imam Mohammad Ibn Saud Islamic University, Riyadh 11623, Saudi Arabia"},{"name":"Department of Mathematics, Faculty of Science, Ain Shams University, Abbassia, Cairo, Egypt"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2024,3,6]]},"reference":[{"key":"S1793830924500137BIB001","first-page":"201","volume":"23","author":"Cahit I.","year":"1987","journal-title":"Ars Comb."},{"key":"S1793830924500137BIB002","doi-asserted-by":"crossref","unstructured":"J. A. Gallian,  A dynamic survey of graph labeling,  Electron. J. Comb. 26th edition, (2023).","DOI":"10.37236\/11668"},{"volume-title":"Graph Theory","year":"1972","author":"Harary F.","key":"S1793830924500137BIB003"},{"key":"S1793830924500137BIB004","doi-asserted-by":"publisher","DOI":"10.55937\/sut\/1360240564"},{"issue":"15","key":"S1793830924500137BIB005","first-page":"733","volume":"7","author":"Ponraj R.","year":"2012","journal-title":"Int. J. Contemp. Math. Sci."},{"key":"S1793830924500137BIB006","volume":"17","author":"Shiu W. C.","year":"2024","journal-title":"Jordan J. Math. Stat."},{"issue":"1","key":"S1793830924500137BIB007","first-page":"155","volume":"23","author":"Sundaram M.","year":"2004","journal-title":"Bull. Pure Appl. Sci."}],"container-title":["Discrete Mathematics, Algorithms and Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S1793830924500137","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,1,22]],"date-time":"2025-01-22T00:58:56Z","timestamp":1737507536000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/10.1142\/S1793830924500137"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,3,6]]},"references-count":7,"journal-issue":{"issue":"01","published-print":{"date-parts":[[2025,1]]}},"alternative-id":["10.1142\/S1793830924500137"],"URL":"https:\/\/doi.org\/10.1142\/s1793830924500137","relation":{},"ISSN":["1793-8309","1793-8317"],"issn-type":[{"type":"print","value":"1793-8309"},{"type":"electronic","value":"1793-8317"}],"subject":[],"published":{"date-parts":[[2024,3,6]]},"article-number":"2450013"}}