{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T13:30:46Z","timestamp":1753882246806,"version":"3.41.2"},"reference-count":15,"publisher":"World Scientific Pub Co Pte Ltd","issue":"04","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Discrete Math. Algorithm. Appl."],"published-print":{"date-parts":[[2025,5]]},"abstract":"<jats:p> Let [Formula: see text] denote a complete graph on [Formula: see text] vertices and [Formula: see text] denote a complete bipartite graph [Formula: see text]. A Bowtie [Formula: see text] is a graph formed by the union of two cycles [Formula: see text] and [Formula: see text] intersecting at a common vertex. A decomposition of a graph [Formula: see text] is a collection of edge-disjoint subgraphs [Formula: see text], such that every edge of G belongs to exactly one [Formula: see text]. Given non-isomorphic subgraphs [Formula: see text] and [Formula: see text] of [Formula: see text], a [Formula: see text] \u2014 multi-decomposition of [Formula: see text] is the decomposition of [Formula: see text] into [Formula: see text] copies of [Formula: see text] and [Formula: see text] copies of [Formula: see text], such that [Formula: see text], for some integers [Formula: see text]. In this paper, the multi-decomposition of [Formula: see text] into [Formula: see text] and [Formula: see text] has been investigated and obtained a necessary and sufficient condition when [Formula: see text]. It is proved that for a given positive integer [Formula: see text], [Formula: see text] can be decomposed into [Formula: see text] copies of [Formula: see text] and [Formula: see text] copies of [Formula: see text] for some pair of non-negative integers [Formula: see text] if and only if [Formula: see text], for all [Formula: see text]. <\/jats:p>","DOI":"10.1142\/s1793830924500666","type":"journal-article","created":{"date-parts":[[2024,7,31]],"date-time":"2024-07-31T02:06:33Z","timestamp":1722391593000},"source":"Crossref","is-referenced-by-count":0,"title":["Multi-decomposition of complete graphs into stars and bowties of size 6"],"prefix":"10.1142","volume":"17","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-4392-4281","authenticated-orcid":false,"given":"P.","family":"Hemalatha","sequence":"first","affiliation":[{"name":"Department of Mathematics, Vellalar College for Women, Erode 638 012, Tamilnadu, India"}]},{"ORCID":"https:\/\/orcid.org\/0009-0001-2972-223X","authenticated-orcid":false,"given":"K.","family":"Ramya","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Government Arts and Science College, Modakkurichi, Erode 638 104, Tamilnadu, India"}]}],"member":"219","published-online":{"date-parts":[[2024,9,10]]},"reference":[{"key":"S1793830924500666BIB001","doi-asserted-by":"publisher","DOI":"10.7151\/dmgt.1719"},{"key":"S1793830924500666BIB002","doi-asserted-by":"publisher","DOI":"10.7151\/dmgt.1820"},{"key":"S1793830924500666BIB003","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-349-03521-2"},{"key":"S1793830924500666BIB004","doi-asserted-by":"publisher","DOI":"10.1016\/j.akcej.2019.09.007"},{"key":"S1793830924500666BIB005","doi-asserted-by":"publisher","DOI":"10.1016\/j.akcej.2019.12.006"},{"key":"S1793830924500666BIB006","doi-asserted-by":"publisher","DOI":"10.1016\/j.disc.2014.05.009"},{"key":"S1793830924500666BIB007","doi-asserted-by":"publisher","DOI":"10.1016\/j.disc.2015.02.019"},{"issue":"2","key":"S1793830924500666BIB009","first-page":"297","volume":"78","author":"Paulraja P.","year":"2020","journal-title":"Australas. 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