{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,17]],"date-time":"2026-04-17T03:41:51Z","timestamp":1776397311460,"version":"3.51.2"},"reference-count":14,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2025,9,2]],"date-time":"2025-09-02T00:00:00Z","timestamp":1756771200000},"content-version":"vor","delay-in-days":244,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"},{"start":{"date-parts":[[2025,1,1]],"date-time":"2025-01-01T00:00:00Z","timestamp":1735689600000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/doi.wiley.com\/10.1002\/tdm_license_1.1"}],"funder":[{"DOI":"10.13039\/501100017170","name":"Thailand Science Research and Innovation","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100017170","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["Journal of Applied Mathematics"],"published-print":{"date-parts":[[2025,1]]},"abstract":"<jats:p>\n                    A graceful labeling of a graph\n                    <jats:italic>G<\/jats:italic>\n                    with\n                    <jats:italic>q<\/jats:italic>\n                    edges is an injection\n                    <jats:italic>f<\/jats:italic>\n                    from the vertices of\n                    <jats:italic>G<\/jats:italic>\n                    to the set {0, 1, \u22ef,\n                    <jats:italic>q<\/jats:italic>\n                    } such that, when each edge\n                    <jats:italic>u<\/jats:italic>\n                    <jats:italic>v<\/jats:italic>\n                    is assigned the label |\n                    <jats:italic>f<\/jats:italic>\n                    (\n                    <jats:italic>u<\/jats:italic>\n                    ) \u2212\n                    <jats:italic>f<\/jats:italic>\n                    (\n                    <jats:italic>v<\/jats:italic>\n                    )|, the resulting edge labels are distinct. A spider graph is a tree with exactly one vertex of degree greater than 2, and this vertex is called the branch vertex. A leg of a spider graph is a path from the branch vertex to a leaf of the tree. We show that there exists graceful labeling of spider graphs with at most five legs.\n                  <\/jats:p>","DOI":"10.1155\/jama\/5826777","type":"journal-article","created":{"date-parts":[[2025,9,3]],"date-time":"2025-09-03T05:22:26Z","timestamp":1756876946000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Graceful Labeling of Spider Graphs With at Most Five Legs"],"prefix":"10.1155","volume":"2025","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-5952-7606","authenticated-orcid":false,"given":"A.","family":"Panpa","sequence":"first","affiliation":[]},{"given":"S.","family":"Imnang","sequence":"additional","affiliation":[]},{"given":"T.","family":"Wasuanankul","sequence":"additional","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2025,9,2]]},"reference":[{"key":"e_1_2_9_1_2","doi-asserted-by":"publisher","DOI":"10.1155\/2021\/9958077"},{"key":"e_1_2_9_2_2","first-page":"349","volume-title":"International Symposium, Theory of Graphs, Rome, July 1966","author":"Rosa A.","year":"1967"},{"key":"e_1_2_9_3_2","first-page":"201","article-title":"Cordial Graphs: A Weaker Version of Graceful and Harmonious Graphs","volume":"23","author":"Cahit I.","year":"1987","journal-title":"Ars Combinatoria"},{"key":"e_1_2_9_4_2","first-page":"3939","article-title":"L(3,2,1)-Labeling Problems on Permutation Graphs","volume":"25","author":"Amanathulla S.","year":"2017","journal-title":"Transylvanian Review"},{"key":"e_1_2_9_5_2","doi-asserted-by":"publisher","DOI":"10.17654\/MS106020515"},{"key":"e_1_2_9_6_2","volume-title":"Proceedings of the Symposium Smolenice","author":"Ringel G.","year":"1964"},{"key":"e_1_2_9_7_2","first-page":"31","article-title":"Further Results on Tree Labelings","volume":"21","author":"Huang C.","year":"1982","journal-title":"Utilitas Mathematica"},{"key":"e_1_2_9_8_2","article-title":"A Dynamic Survey of Graph Labeling","volume":"16","author":"Gallian J. A.","year":"2015","journal-title":"Electronic Journal of Combinatorics"},{"key":"e_1_2_9_9_2","doi-asserted-by":"publisher","DOI":"10.1155\/S1110757X04310065"},{"key":"e_1_2_9_10_2","doi-asserted-by":"publisher","DOI":"10.1016\/B978-1-4832-3187-7.50008-8"},{"key":"e_1_2_9_11_2","first-page":"67","article-title":"Labeling Snakes","volume":"3","author":"Rosa A.","year":"1977","journal-title":"Ars Combinatoria"},{"key":"e_1_2_9_12_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.disc.2007.03.046"},{"key":"e_1_2_9_13_2","unstructured":"StantonR.andZarnkeC. Labeling of Balanced Trees Proc. 4th Southeast Conf. Combin. Graph Theory Comput. 1973 479\u2013495."},{"key":"e_1_2_9_14_2","doi-asserted-by":"publisher","DOI":"10.1007\/BFb0102685"}],"container-title":["Journal of Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1155\/jama\/5826777","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/full-xml\/10.1155\/jama\/5826777","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1155\/jama\/5826777","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,17]],"date-time":"2026-04-17T02:44:14Z","timestamp":1776393854000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1155\/jama\/5826777"}},"subtitle":[],"editor":[{"given":"Arpan","family":"Hazra","sequence":"additional","affiliation":[]}],"short-title":[],"issued":{"date-parts":[[2025,1]]},"references-count":14,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2025,1]]}},"alternative-id":["10.1155\/jama\/5826777"],"URL":"https:\/\/doi.org\/10.1155\/jama\/5826777","archive":["Portico"],"relation":{},"ISSN":["1110-757X","1687-0042"],"issn-type":[{"value":"1110-757X","type":"print"},{"value":"1687-0042","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,1]]},"assertion":[{"value":"2024-07-09","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2025-07-28","order":2,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2025-09-02","order":3,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}],"article-number":"5826777"}}