{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,7]],"date-time":"2026-04-07T10:59:38Z","timestamp":1775559578605,"version":"3.50.1"},"reference-count":0,"publisher":"World Scientific Pub Co Pte Ltd","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Discrete Math. Algorithm. Appl."],"abstract":"<jats:p>We consider the notions of sum graph and of relaxed sum graph over a magma, give several examples and results of these families of graphs over some natural magmas. We classify the cycles that are sum graphs for the magma of the subsets of a set with the operation of union, determine the abelian groups that provide a sum labeling of [Formula: see text], and show that [Formula: see text] is a sum graph over the abelian group [Formula: see text], where [Formula: see text] is the corresponding Fibonacci number. For integral sum graphs, we give a linear upper bound for the radius of matchings, improving Harary\u2019s labeling for this family of graphs, and give the exact radius for the family of totally disconnected graphs. We found integer labelings for the 4D-cube, giving a negative answer to a question of Melnikov and Pyatikin, actually showing that the 4D-cube has infinitely many primitive labelings. We have also obtained some new results on mod sum graphs and relaxed sum graphs. Finally, we show that the direct product operation is closed for strong integral sum graphs.<\/jats:p>","DOI":"10.1142\/s1793830926500394","type":"journal-article","created":{"date-parts":[[2026,3,20]],"date-time":"2026-03-20T08:35:54Z","timestamp":1773995754000},"source":"Crossref","is-referenced-by-count":0,"title":["On sum graphs over some magmas"],"prefix":"10.1142","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-7595-7275","authenticated-orcid":false,"given":"Ant\u00f3nio","family":"Machiavelo","sequence":"first","affiliation":[{"name":"CMUP, Faculdade de Ci\u00eancias da Universidade do Porto, 4169-007 Porto, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9668-0917","authenticated-orcid":false,"given":"Rog\u00e9rio","family":"Reis","sequence":"additional","affiliation":[{"name":"CMUP, Faculdade de Ci\u00eancias da Universidade do Porto, 4169-007 Porto, Portugal"}]}],"member":"219","published-online":{"date-parts":[[2026,4,7]]},"container-title":["Discrete Mathematics, Algorithms and Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S1793830926500394","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,7]],"date-time":"2026-04-07T10:06:07Z","timestamp":1775556367000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/10.1142\/S1793830926500394"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,4,7]]},"references-count":0,"alternative-id":["10.1142\/S1793830926500394"],"URL":"https:\/\/doi.org\/10.1142\/s1793830926500394","relation":{},"ISSN":["1793-8309","1793-8317"],"issn-type":[{"value":"1793-8309","type":"print"},{"value":"1793-8317","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,4,7]]},"article-number":"2650039"}}