{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T17:42:40Z","timestamp":1760118160412,"version":"build-2065373602"},"reference-count":13,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2024,12,26]],"date-time":"2024-12-26T00:00:00Z","timestamp":1735171200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>A graph, G=(V,E), is edge odd graceful if it possesses edge odd graceful labeling. This labeling is defined as a bijection g:E(G)\u2192{1,3,\u2026,2m\u22121}, from which an injective transformation is derived, g*:V(G)\u2192{1,2,3,\u2026,2m\u22121}, from the rule that the image of u\u2208V(G) under g* is \u2211uv\u2208E(G)g(uv)mod(2m). The main objective of this manuscript is to introduce new classes of planar graphs, namely water wheel graphs, WWn; triangulated water wheel graphs, TWn; closed water wheel graphs, CWn; and closed triangulated water wheel graphs, CTn. Furthermore, we specify conditions for these graphs to allow for edge odd graceful labelings.<\/jats:p>","DOI":"10.3390\/axioms14010005","type":"journal-article","created":{"date-parts":[[2024,12,26]],"date-time":"2024-12-26T21:13:18Z","timestamp":1735247598000},"page":"5","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["The Edge Odd Graceful Labeling of Water Wheel Graphs"],"prefix":"10.3390","volume":"14","author":[{"given":"Mohammed","family":"Aljohani","sequence":"first","affiliation":[{"name":"Department of Mathematics, Faculty of Science, Taibah University, Al-Madinah 41411, Saudi Arabia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3809-2521","authenticated-orcid":false,"given":"Salama Nagy","family":"Daoud","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Science, Taibah University, Al-Madinah 41411, Saudi Arabia"},{"name":"Department of Mathematics and Computer Sciences, Faculty of Science, Menoufia University, Shebin El Kom 32511, Egypt"}]}],"member":"1968","published-online":{"date-parts":[[2024,12,26]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"562","DOI":"10.1109\/PROC.1977.10517","article-title":"Applications of numbered undirected graphs","volume":"4","author":"Bloom","year":"1977","journal-title":"Proc. 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Graphs Comb."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"10568","DOI":"10.1109\/ACCESS.2018.2889293","article-title":"edge-odd-graceful Labeling of Cylinder and Torus Grid Graphs","volume":"7","author":"Daoud","year":"2018","journal-title":"IEEE Access"},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Aljohani, M., and Daoud, S.N. (2024). Edge Odd Graceful Labeling in Some Wheel-Related Graphs. Mathematics, 12.","DOI":"10.3390\/math12081203"}],"container-title":["Axioms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2075-1680\/14\/1\/5\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T17:00:39Z","timestamp":1760115639000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2075-1680\/14\/1\/5"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,12,26]]},"references-count":13,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2025,1]]}},"alternative-id":["axioms14010005"],"URL":"https:\/\/doi.org\/10.3390\/axioms14010005","relation":{},"ISSN":["2075-1680"],"issn-type":[{"type":"electronic","value":"2075-1680"}],"subject":[],"published":{"date-parts":[[2024,12,26]]}}}