{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,21]],"date-time":"2026-01-21T12:30:30Z","timestamp":1768998630261,"version":"3.49.0"},"reference-count":11,"publisher":"Springer Science and Business Media LLC","issue":"6","license":[{"start":{"date-parts":[[2020,9,3]],"date-time":"2020-09-03T00:00:00Z","timestamp":1599091200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2020,9,3]],"date-time":"2020-09-03T00:00:00Z","timestamp":1599091200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"funder":[{"DOI":"10.13039\/501100001807","name":"FAPESP","doi-asserted-by":"crossref","award":["2014\/16987-1"],"award-info":[{"award-number":["2014\/16987-1"]}],"id":[{"id":"10.13039\/501100001807","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/501100001807","name":"FAPESP","doi-asserted-by":"crossref","award":["2015\/03372-1"],"award-info":[{"award-number":["2015\/03372-1"]}],"id":[{"id":"10.13039\/501100001807","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/501100000038","name":"NSERC","doi-asserted-by":"crossref","award":["41705-2014 057082"],"award-info":[{"award-number":["41705-2014 057082"]}],"id":[{"id":"10.13039\/501100000038","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/501100001807","name":"FAPESP","doi-asserted-by":"crossref","award":["2014\/16861-8"],"award-info":[{"award-number":["2014\/16861-8"]}],"id":[{"id":"10.13039\/501100001807","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Graphs and Combinatorics"],"published-print":{"date-parts":[[2020,11]]},"DOI":"10.1007\/s00373-020-02226-0","type":"journal-article","created":{"date-parts":[[2020,9,3]],"date-time":"2020-09-03T12:03:33Z","timestamp":1599134613000},"page":"1655-1673","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["On 0-Rotatable Graceful Caterpillars"],"prefix":"10.1007","volume":"36","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-6177-403X","authenticated-orcid":false,"given":"At\u00edlio G.","family":"Luiz","sequence":"first","affiliation":[]},{"given":"C. N.","family":"Campos","sequence":"additional","affiliation":[]},{"given":"R. Bruce","family":"Richter","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2020,9,3]]},"reference":[{"key":"2226_CR1","doi-asserted-by":"publisher","first-page":"65","DOI":"10.1016\/j.dam.2015.05.031","volume":"198","author":"D Anick","year":"2016","unstructured":"Anick, D.: Counting graceful labelings of trees: a theoretical and empirical study. Discret. Appl. Math. 198, 65\u201381 (2016)","journal-title":"Discret. Appl. Math."},{"key":"2226_CR2","first-page":"183","volume":"51","author":"AJ Broersma","year":"1999","unstructured":"Broersma, A.J., Hoede, C.: Another equivalent of the graceful tree conjecture. Ars Combinatoria 51, 183\u2013192 (1999)","journal-title":"Ars Combinatoria"},{"issue":"1\u20133","key":"2226_CR3","doi-asserted-by":"publisher","first-page":"193","DOI":"10.1016\/S0012-365X(03)00152-3","volume":"277","author":"FV Bussel","year":"2004","unstructured":"Bussel, F.V.: 0-Centred and 0-ubiquitously graceful trees. Discret. Math. 277(1\u20133), 193\u2013218 (2004)","journal-title":"Discret. Math."},{"issue":"24","key":"2226_CR4","doi-asserted-by":"publisher","first-page":"3161","DOI":"10.1016\/j.disc.2007.03.046","volume":"307","author":"R Cattell","year":"2007","unstructured":"Cattell, R.: Graceful labellings of paths. Discret. Math. 307(24), 3161\u20133176 (2007)","journal-title":"Discret. Math."},{"key":"2226_CR5","first-page":"239","volume":"11","author":"FRK Chung","year":"1981","unstructured":"Chung, F.R.K., Hwang, F.K.: Rotatable graceful graphs. Ars Combinatoria 11, 239\u2013250 (1981)","journal-title":"Ars Combinatoria"},{"key":"2226_CR6","first-page":"1","volume":"DS6","author":"JA Gallian","year":"2018","unstructured":"Gallian, J.A.: A dynamic survey of graph labeling. Electron. J. Combinatorics DS6, 1\u2013502 (2018)","journal-title":"Electron. J. Combinatorics"},{"issue":"1\u20133","key":"2226_CR7","doi-asserted-by":"publisher","first-page":"133","DOI":"10.1016\/S0012-365X(00)00233-8","volume":"233","author":"P Hrn\u010diar","year":"2001","unstructured":"Hrn\u010diar, P., Haviar, A.: All trees of diameter five are graceful. Discret. Math. 233(1\u20133), 133\u2013150 (2001)","journal-title":"Discret. Math."},{"key":"2226_CR8","first-page":"31","volume":"21","author":"C Huang","year":"1982","unstructured":"Huang, C., Kotzig, A., Rosa, A.: Further results on tree labellings. Util. Math. 21, 31\u201348 (1982)","journal-title":"Util. Math."},{"key":"2226_CR9","first-page":"155","volume":"74","author":"D Mishra","year":"2007","unstructured":"Mishra, D., Panigrahi, P.: Some graceful lobsters with both odd and even degree vertices on the central path. Util. Math. 74, 155\u2013177 (2007)","journal-title":"Util. Math."},{"key":"2226_CR10","first-page":"349","volume-title":"Theory of Graphs (International Symposium, Rome, Italy, 1966)","author":"A Rosa","year":"1967","unstructured":"Rosa, A.: On certain valuations of the vertices of a graph. Theory of Graphs (International Symposium, Rome, Italy, 1966), pp. 349\u2013355. Gordon and Breach, New York (1967)"},{"key":"2226_CR11","first-page":"67","volume":"3","author":"A Rosa","year":"1977","unstructured":"Rosa, A.: Labeling snakes. Ars Combinatoria 3, 67\u201373 (1977)","journal-title":"Ars Combinatoria"}],"container-title":["Graphs and Combinatorics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00373-020-02226-0.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s00373-020-02226-0\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00373-020-02226-0.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,9,3]],"date-time":"2021-09-03T22:24:08Z","timestamp":1630707848000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s00373-020-02226-0"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,9,3]]},"references-count":11,"journal-issue":{"issue":"6","published-print":{"date-parts":[[2020,11]]}},"alternative-id":["2226"],"URL":"https:\/\/doi.org\/10.1007\/s00373-020-02226-0","relation":{},"ISSN":["0911-0119","1435-5914"],"issn-type":[{"value":"0911-0119","type":"print"},{"value":"1435-5914","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,9,3]]},"assertion":[{"value":"11 March 2019","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"14 August 2020","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"3 September 2020","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}