{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,9]],"date-time":"2025-10-09T00:37:42Z","timestamp":1759970262394,"version":"build-2065373602"},"reference-count":20,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2025,1,12]],"date-time":"2025-01-12T00:00:00Z","timestamp":1736640000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>Graph labeling is the process of assigning labels to vertices and edges under certain conditions. This paper investigates the graceful local antimagic labeling of various graph families, excluding symmetric labelings, using computational experiments and Python-based algorithms. Through these experiments, we identify new results and patterns within specific graph classes. The study expands on the existing literature by offering computational evidence, proposing algorithms for the verification of labelings, and exploring the relationship between the local antimagic labeling and the chromatic number. Our results increase the understanding of graph labeling and offer insights into its computational aspects.<\/jats:p>","DOI":"10.3390\/sym17010108","type":"journal-article","created":{"date-parts":[[2025,1,13]],"date-time":"2025-01-13T04:01:52Z","timestamp":1736740912000},"page":"108","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Graceful Local Antimagic Labeling of Graphs: A Pattern Analysis Using Python"],"prefix":"10.3390","volume":"17","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-7654-4061","authenticated-orcid":false,"given":"Luqman","family":"Alam","sequence":"first","affiliation":[{"name":"Abdus Salam School of Mathematical Sciences, GC Lahore, Lahore 56000, Punjab, Pakistan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8432-9836","authenticated-orcid":false,"given":"Andrea","family":"Semani\u010dov\u00e1-Fe\u0148ov\u010d\u00edkov\u00e1","sequence":"additional","affiliation":[{"name":"Department of Applied Mathematics and Informatics, Technical University, 042 00 Kosice, Slovakia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8042-1806","authenticated-orcid":false,"given":"Ioan-Lucian","family":"Popa","sequence":"additional","affiliation":[{"name":"Department of Computing, Mathematics and Electronics, 1 Decembrie 1918 University of Alba Iulia, 510009 Alba Iulia, Romania"},{"name":"Faculty of Mathematics and Computer Science, Transilvania University of Brasov, Iuliu Maniu Street 50, 500091 Brasov, Romania"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2025,1,12]]},"reference":[{"key":"ref_1","unstructured":"Chartrand, G., and Zhang, P. (2005). Introduction to Graph Theory, McGraw-Hill."},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Wallis, W.D. (2001). Magic Graphs, Birkh\u00e4user.","DOI":"10.1007\/978-1-4612-0123-6"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"451","DOI":"10.4153\/CMB-1970-084-1","article-title":"Magic valuations of finite graphs","volume":"13","author":"Kotzig","year":"1970","journal-title":"Canad. Math. Bull."},{"key":"ref_4","unstructured":"Golomb, S.W. (1973). Labeling of graphs. Recent Progress in Combinatorics, Academic Press."},{"key":"ref_5","first-page":"162","article-title":"Problem 25, in Theory of graphs and its applications, Proc. Symposium Smolenice","volume":"1963","author":"Ringel","year":"1964","journal-title":"Prague"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"195","DOI":"10.1016\/0012-365X(91)90255-Z","article-title":"On Skolem graceful graphs","volume":"93","author":"Lee","year":"1991","journal-title":"Discrete Math."},{"key":"ref_7","first-page":"181","article-title":"On d-graceful graphs","volume":"13","author":"Maheo","year":"1982","journal-title":"Ars Combin."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"39","DOI":"10.1016\/0012-365X(90)90285-P","article-title":"Strongly graceful graphs","volume":"29","author":"Maheo","year":"1980","journal-title":"Discrete Math."},{"key":"ref_9","unstructured":"Slater, P.J. (1982, January 15\u201317). On k-graceful graphs. Proceedings of the 13th SEICCGTC 1982, Boca Raton, FL, USA."},{"key":"ref_10","first-page":"377","article-title":"Graceful unicyclic graphs","volume":"17","author":"Truszczynski","year":"1984","journal-title":"Demonstr. Math."},{"key":"ref_11","first-page":"1","article-title":"A Dynamic Survey of Graph Labeling","volume":"18","author":"Gallian","year":"2011","journal-title":"Electron. J. Combin."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"483","DOI":"10.1002\/jcd.21296","article-title":"2-Starters, Graceful Labelings, and a Doubling Construction for the Oberwolfach Problem","volume":"20","author":"Buratti","year":"2012","journal-title":"J. Combin. Des."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"105","DOI":"10.1016\/j.jcta.2022.105611","article-title":"On the Oberwolfach problem for single-flip 2-factors via graceful labelings","volume":"189","author":"Burgess","year":"2022","journal-title":"J. Comb. Theory A"},{"key":"ref_14","first-page":"107","article-title":"Supermagic and antimagic graphs","volume":"21","author":"Hartsfield","year":"1989","journal-title":"J. Recreat. Math."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"13","DOI":"10.1007\/s00010-022-00930-1","article-title":"On graceful antimagic graphs","volume":"97","author":"Ahmed","year":"2023","journal-title":"Aequat. Math."},{"key":"ref_16","unstructured":"Hartsfield, N., and Ringel, G. (1994). Pearls in Graph Theory, Academic Press, Inc."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"28","DOI":"10.1002\/jgt.21836","article-title":"Regular graphs of odd degree are antimagic","volume":"80","author":"Cranston","year":"2015","journal-title":"J. Graph Theory"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"139","DOI":"10.1007\/s11786-015-0218-0","article-title":"Antimagic labelings of join graphs","volume":"9","author":"Miller","year":"2015","journal-title":"Math. Comput. Sci."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"275","DOI":"10.1007\/s00373-017-1758-7","article-title":"Local antimagic vertex coloring of a graph","volume":"33","author":"Arumugam","year":"2017","journal-title":"Graphs Combin."},{"key":"ref_20","first-page":"1","article-title":"Proof of a local antimagic conjecture","volume":"20","author":"Haslegrave","year":"2018","journal-title":"Discr. Math. Theor. Comp. Sci."}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/17\/1\/108\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,8]],"date-time":"2025-10-08T10:27:17Z","timestamp":1759919237000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/17\/1\/108"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,1,12]]},"references-count":20,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2025,1]]}},"alternative-id":["sym17010108"],"URL":"https:\/\/doi.org\/10.3390\/sym17010108","relation":{},"ISSN":["2073-8994"],"issn-type":[{"type":"electronic","value":"2073-8994"}],"subject":[],"published":{"date-parts":[[2025,1,12]]}}}