{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,10,22]],"date-time":"2023-10-22T12:12:00Z","timestamp":1697976720982},"reference-count":8,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2006,10,3]],"date-time":"2006-10-03T00:00:00Z","timestamp":1159833600000},"content-version":"vor","delay-in-days":7886,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Journal of Graph Theory"],"published-print":{"date-parts":[[1985,3]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>For a nonempty graph, G, we define p(G) and r(G) to be respectively the minimum order and minimum degree of regularity among all connected regular graphs <jats:italic>H<\/jats:italic> having a nontrivial decomposition into subgraphs isomorphic to G. By f(G), we denote the least integer t for which there is a connected regular graph H having a decomposition into t subgraphs isomorphic to G. In this article, the values of these parameters are determined for complete graphs, cycles, and stars. Furthermore, we show that \u0394(<jats:italic>T<\/jats:italic>) \u2a7d <jats:italic>r<\/jats:italic>(<jats:italic>T<\/jats:italic>) \u2a7d \u03b4 (<jats:italic>T<\/jats:italic>) + 1 for every tree <jats:italic>T<\/jats:italic>. and <jats:italic>r<\/jats:italic>(<jats:italic>T<\/jats:italic>) \u0394(<jats:italic>T<\/jats:italic>) if the maximum degree \u0394(<jats:italic>T<\/jats:italic>) is even.<\/jats:p>","DOI":"10.1002\/jgt.3190090108","type":"journal-article","created":{"date-parts":[[2007,5,29]],"date-time":"2007-05-29T07:48:01Z","timestamp":1180424881000},"page":"105-117","source":"Crossref","is-referenced-by-count":1,"title":["On smallest regular graphs with a given isopart"],"prefix":"10.1002","volume":"9","author":[{"given":"John Frederick","family":"Fink","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2006,10,3]]},"reference":[{"key":"e_1_2_1_2_2","volume-title":"Graphs & Digraphs","author":"Behzad M.","year":"1979"},{"key":"e_1_2_1_3_2","unstructured":"J. F.Fink Every graph is an induced isopart of a connected regular graph. Submitted for publication."},{"key":"e_1_2_1_4_2","unstructured":"J. F.FinkandS.Ruiz Every graph is an induced isopart of a circulant. Submitted for publication."},{"key":"e_1_2_1_5_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF01456961"},{"key":"e_1_2_1_6_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF02392606"},{"key":"e_1_2_1_7_2","doi-asserted-by":"publisher","DOI":"10.1515\/crll.1859.56.326"},{"key":"e_1_2_1_8_2","series-title":"Internat. Sympos. Rome, 1966","first-page":"349","volume-title":"Theory of Graphs","author":"Rosal A.","year":"1967"},{"key":"e_1_2_1_9_2","unstructured":"R. M.Wilson Decompositions of complete graphs into subgraphs isomorphic to a given graph.Proceedings of the Fifth British Combinatorial Conference(Univ. Aberdeen Aberdeen 1975)647\u2013659.Congresses Numeratium No. XV Utilitas Math. Winnipeg Man. (1976)."}],"container-title":["Journal of Graph Theory"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fjgt.3190090108","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/jgt.3190090108","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,10,21]],"date-time":"2023-10-21T05:46:31Z","timestamp":1697867191000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/jgt.3190090108"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1985,3]]},"references-count":8,"journal-issue":{"issue":"1","published-print":{"date-parts":[[1985,3]]}},"alternative-id":["10.1002\/jgt.3190090108"],"URL":"https:\/\/doi.org\/10.1002\/jgt.3190090108","archive":["Portico"],"relation":{},"ISSN":["0364-9024","1097-0118"],"issn-type":[{"value":"0364-9024","type":"print"},{"value":"1097-0118","type":"electronic"}],"subject":[],"published":{"date-parts":[[1985,3]]}}}