{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,20]],"date-time":"2026-01-20T00:56:41Z","timestamp":1768870601221,"version":"3.49.0"},"reference-count":0,"publisher":"Combinatorial Press","issue":"1","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Ars Comb."],"published-print":{"date-parts":[[2024,6,30]]},"abstract":"<jats:p>In this paper, we introduce graceful and near graceful labellings of several families of windmills. In particular, we use Skolem-type sequences to prove (near) graceful labellings exist for windmills with \\(C_{3}\\) and \\(C_{4}\\) vanes, and infinite families of \\(3,5\\)-windmills and \\(3,6\\)-windmills. Furthermore, we offer a new solution showing that the graph obtained from the union of \\(t\\) 5-cycles with one vertex in common (\\(C_{5}^{t}\\)) is graceful if and only if \\(t \\equiv 0, 3 \\pmod{4}\\) and near graceful when \\(t \\equiv 1, 2 \\pmod{4}\\).<\/jats:p>","DOI":"10.61091\/ars159-11","type":"journal-article","created":{"date-parts":[[2024,7,10]],"date-time":"2024-07-10T05:14:41Z","timestamp":1720588481000},"page":"109-131","source":"Crossref","is-referenced-by-count":2,"title":["Graceful Labellings of Variable Windmills Using Skolem-type Sequences"],"prefix":"10.61091","volume":"159","author":[{"name":"Department of Mathematics and Statistics, St. John\u2019s Campus, Memorial University of Newfoundland, St. John\u2019s, Newfoundland, Canada","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ahmad H.","family":"Alkasasbeh","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Danny","family":"Dyer","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"name":"Department of Mathematics and Statistics, St. John\u2019s Campus, Memorial University of Newfoundland, St. John\u2019s, Newfoundland, Canada","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jared","family":"Howell","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"name":"School of Science and the Environment, Grenfell Campus, Memorial University of Newfoundland, Corner Brook, Newfoundland, Canada","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"39747","published-online":{"date-parts":[[2024,6,30]]},"container-title":["Ars Combinatoria"],"original-title":[],"deposited":{"date-parts":[[2024,7,10]],"date-time":"2024-07-10T05:14:52Z","timestamp":1720588492000},"score":1,"resource":{"primary":{"URL":"https:\/\/combinatorialpress.com\/ars-articles\/volume-159\/graceful-labellings-of-variable-windmills-using-skolem-type-sequences\/109"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,6,30]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2024,6,30]]},"published-print":{"date-parts":[[2024,6,30]]}},"URL":"https:\/\/doi.org\/10.61091\/ars159-11","relation":{},"ISSN":["0381-7032","2817-5204"],"issn-type":[{"value":"0381-7032","type":"print"},{"value":"2817-5204","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,6,30]]}}}