{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,6,2]],"date-time":"2024-06-02T15:10:22Z","timestamp":1717341022759},"reference-count":14,"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":[[2015,3]]},"abstract":"<jats:p>Partition of G into edge-disjoint H-factors is called an H-factorization of G. Shehzad Afzal and Clemens Brand have factorized graphs into factors which are isomorphic to triangulated Cartesian product of two subgraphs. Also they have discussed properties of triangulated Cartesian product of more than two graphs. In this paper, we show that the necessary conditions mn \u2261 0 (mod 3), m, n are odd and 3(mn + m + n - 3) \u2261 0 (mod 8) are sufficient for the existence of a P<jats:sub>3<\/jats:sub>-factorization of K<jats:sub>m<\/jats:sub>\u29c5 K<jats:sub>n<\/jats:sub>, where \u29c5 denotes triangulated Cartesian product of graphs, if one of the following holds:<\/jats:p><jats:p>(i) m \u2261 9 (mod 12), n = 5, 13 and 17,<\/jats:p><jats:p>(ii) m \u2261 9 (mod 12), n<jats:sup>s<\/jats:sup>, s &gt; 1, n = 5, 13 and 17,<\/jats:p><jats:p>(iii) m \u2261 9 (mod 12), n = p<jats:sup>s<\/jats:sup>q<jats:sup>t<\/jats:sup>for all s, t \u2265 1, where p = 5, 13 and q = 13, 17, p \u2260 q,<\/jats:p><jats:p>(iv) m \u2261 9 (mod 12), n \u2261 9 (mod 12).<\/jats:p>","DOI":"10.1142\/s1793830914500669","type":"journal-article","created":{"date-parts":[[2014,9,16]],"date-time":"2014-09-16T08:44:37Z","timestamp":1410857077000},"page":"1450066","source":"Crossref","is-referenced-by-count":1,"title":["P<sub>3<\/sub>-factorization of triangulated Cartesian product of complete graphs"],"prefix":"10.1142","volume":"07","author":[{"given":"A.","family":"Tamil Elakkiya","sequence":"first","affiliation":[{"name":"Department of Mathematics, Periyar University, Salem, Tamil Nadu, India"}]},{"given":"A.","family":"Muthusamy","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Periyar University, Salem, Tamil Nadu, India"}]}],"member":"219","published-online":{"date-parts":[[2015,2,2]]},"reference":[{"key":"rf1","doi-asserted-by":"publisher","DOI":"10.1016\/j.disc.2011.08.001"},{"key":"rf2","doi-asserted-by":"publisher","DOI":"10.1007\/978-94-009-0517-7_2"},{"key":"rf3","doi-asserted-by":"crossref","DOI":"10.1093\/oso\/9780198500292.001.0001","volume-title":"Combinatorial Designs and Tournaments","author":"Anderson I.","year":"1997"},{"key":"rf4","first-page":"60","volume":"63","author":"Chitra V.","year":"2011","journal-title":"Bull. Inst. Combin. Appl."},{"key":"rf5","doi-asserted-by":"publisher","DOI":"10.1007\/s11425-006-0289-0"},{"key":"rf6","first-page":"115","volume":"141","author":"Haggkvist R.","year":"1989","journal-title":"London Math. Soc. Lecture Note Ser."},{"key":"rf7","volume-title":"Design Theory","author":"Lindner C. C.","year":"2009"},{"key":"rf9","doi-asserted-by":"publisher","DOI":"10.1016\/S0012-365X(98)00176-9"},{"key":"rf10","first-page":"127","volume":"84","author":"Sampath Kumar R.","year":"2013","journal-title":"J. Combin. Math. Combin. Comput."},{"key":"rf11","doi-asserted-by":"publisher","DOI":"10.1142\/S1793830914500190"},{"key":"rf12","doi-asserted-by":"publisher","DOI":"10.1016\/0012-365X(88)90227-0"},{"key":"rf13","doi-asserted-by":"publisher","DOI":"10.1007\/BF01788695"},{"key":"rf14","doi-asserted-by":"publisher","DOI":"10.1016\/j.disc.2006.09.046"},{"key":"rf15","doi-asserted-by":"publisher","DOI":"10.1016\/0012-365X(93)90305-D"}],"container-title":["Discrete Mathematics, Algorithms and Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S1793830914500669","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,6,2]],"date-time":"2024-06-02T14:53:46Z","timestamp":1717340026000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S1793830914500669"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,2,2]]},"references-count":14,"journal-issue":{"issue":"01","published-online":{"date-parts":[[2015,2,2]]},"published-print":{"date-parts":[[2015,3]]}},"alternative-id":["10.1142\/S1793830914500669"],"URL":"https:\/\/doi.org\/10.1142\/s1793830914500669","relation":{},"ISSN":["1793-8309","1793-8317"],"issn-type":[{"value":"1793-8309","type":"print"},{"value":"1793-8317","type":"electronic"}],"subject":[],"published":{"date-parts":[[2015,2,2]]}}}