{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,11,13]],"date-time":"2023-11-13T00:33:21Z","timestamp":1699835601190},"reference-count":2,"publisher":"Wiley","issue":"2","license":[{"start":{"date-parts":[[2006,10,3]],"date-time":"2006-10-03T00:00:00Z","timestamp":1159833600000},"content-version":"vor","delay-in-days":9986,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Journal of Graph Theory"],"published-print":{"date-parts":[[1979,6]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>Given a graph \u0393 an abelian group <jats:italic>G<\/jats:italic>, and a labeling of the vertices of \u0393 with elements of <jats:italic>G<\/jats:italic>, necessary and sufficient conditions are stated for the existence of a labeling of the edges in which the label of each vertex equals the product of the labels of its incident edges. Such an edge labeling is called compatible. For vertex labelings satisfying these conditions, the set of compatible edge labelings is enumerated.<\/jats:p>","DOI":"10.1002\/jgt.3190030205","type":"journal-article","created":{"date-parts":[[2007,5,26]],"date-time":"2007-05-26T10:26:03Z","timestamp":1180175163000},"page":"135-140","source":"Crossref","is-referenced-by-count":2,"title":["Group labelings of graphs"],"prefix":"10.1002","volume":"3","author":[{"given":"Paul H.","family":"Edelman","sequence":"first","affiliation":[]},{"given":"Michael","family":"Saks","sequence":"additional","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2006,10,3]]},"reference":[{"key":"e_1_2_1_2_2","series-title":"Ter Science TR 75\u2013239","first-page":"19","volume-title":"The complexity of resolution procedures for theorem providing in the prepositional calculus","author":"Galil Z."},{"key":"e_1_2_1_3_2","first-page":"115","volume-title":"Structures in Constructive Mathematics and Mathematical Logic, Part II","author":"Tseitin G. S.","year":"1968"}],"container-title":["Journal of Graph Theory"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fjgt.3190030205","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/jgt.3190030205","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,11,12]],"date-time":"2023-11-12T09:36:22Z","timestamp":1699781782000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/jgt.3190030205"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1979,6]]},"references-count":2,"journal-issue":{"issue":"2","published-print":{"date-parts":[[1979,6]]}},"alternative-id":["10.1002\/jgt.3190030205"],"URL":"https:\/\/doi.org\/10.1002\/jgt.3190030205","archive":["Portico"],"relation":{},"ISSN":["0364-9024","1097-0118"],"issn-type":[{"value":"0364-9024","type":"print"},{"value":"1097-0118","type":"electronic"}],"subject":[],"published":{"date-parts":[[1979,6]]}}}