{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:43:01Z","timestamp":1753893781023,"version":"3.41.2"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"1","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>We investigate the existence of edge-magic labellings of countably infinite graphs by abelian groups. We show for that for a large class of abelian groups, including the integers ${\\Bbb Z}$, there is such a labelling whenever the graph has an infinite set of disjoint edges.  A graph without an infinite set of disjoint edges must be some subgraph of $H + {\\cal I}$, where $H$ is some finite graph and ${\\cal I}$ is a countable set of isolated vertices. Using power series of rational functions, we show that any edge-magic ${\\Bbb Z}$-labelling of $H + {\\cal I}$ has almost all vertex labels making up pairs of half-modulus classes.  We also classify all possible edge-magic ${\\Bbb Z}$-labellings of $H + {\\cal I}$ under the assumption that the vertices of the finite graph are labelled consecutively.<\/jats:p>","DOI":"10.37236\/1118","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T04:56:16Z","timestamp":1578718576000},"source":"Crossref","is-referenced-by-count":4,"title":["Edge-Magic Group Labellings of Countable Graphs"],"prefix":"10.37236","volume":"13","author":[{"given":"Nicholas","family":"Cavenagh","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Diana","family":"Combe","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Adrian M.","family":"Nelson","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"23455","published-online":{"date-parts":[[2006,10,27]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v13i1r92\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v13i1r92\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,18]],"date-time":"2020-01-18T04:07:14Z","timestamp":1579320434000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v13i1r92"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2006,10,27]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2006,1,7]]}},"URL":"https:\/\/doi.org\/10.37236\/1118","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2006,10,27]]},"article-number":"R92"}}