{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T03:37:16Z","timestamp":1760240236289,"version":"build-2065373602"},"reference-count":26,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2019,4,22]],"date-time":"2019-04-22T00:00:00Z","timestamp":1555891200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100002403","name":"Taibah University","doi-asserted-by":"publisher","award":["2019"],"award-info":[{"award-number":["2019"]}],"id":[{"id":"10.13039\/501100002403","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>Edge even graceful labeling (e.e.g., l.) of graphs is a modular technique of edge labeling of graphs, introduced in 2017. An e.e.g., l. of simple finite undirected graph     G = ( V ( G ) , E ( G ) )     of order     P =  |  ( V ( G )  |      and size     q =  |  E ( G )  |      is a bijection     f : E ( G ) \u2192 { 2 , 4 , \u2026 , 2 q }    , such that when each vertex     v \u2208 V ( G )     is assigned the modular sum of the labels (images of    f   ) of the edges incident to    v   , the resulting vertex labels are distinct     mod 2 r    , where     r = max ( p , q )    . In this work, the family of cylinder grid graphs are studied. Explicit formulas of e.e.g., l. for all of the cases of each member of this family have been proven.<\/jats:p>","DOI":"10.3390\/sym11040584","type":"journal-article","created":{"date-parts":[[2019,4,22]],"date-time":"2019-04-22T11:02:53Z","timestamp":1555930973000},"page":"584","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Edge Even Graceful Labeling of Cylinder Grid Graph"],"prefix":"10.3390","volume":"11","author":[{"given":"Ahmed A.","family":"Elsonbaty","sequence":"first","affiliation":[{"name":"Department of Mathematics, Faculty of Science, Taibah University, Al-Madinah 41411, Saudi Arabia"},{"name":"Department of Mathematics, Faculty of Science, Ain Shams University, Cairo 11566, Egypt"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"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 Compuer Science, Faculty of Science, Menoufia University, Shebin El Kom 32511, Egypt"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2019,4,22]]},"reference":[{"key":"ref_1","unstructured":"Acharya, B.D., Arumugam, S., and Rosa, A. 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