{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,10,27]],"date-time":"2023-10-27T05:40:23Z","timestamp":1698385223174},"reference-count":4,"publisher":"Wiley","issue":"3","license":[{"start":{"date-parts":[[2006,10,6]],"date-time":"2006-10-06T00:00:00Z","timestamp":1160092800000},"content-version":"vor","delay-in-days":4176,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Journal of Graph Theory"],"published-print":{"date-parts":[[1995,5]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>The edge reconstruction number of a graph <jats:italic>G, RN(G)<\/jats:italic>, is the minimum number of edge deleted subgraphs required to determine <jats:italic>G<\/jats:italic> up to isomorphism. We prove the following results for a disconnected graph <jats:italic>G<\/jats:italic> with at least two nontrivial components. If <jats:italic>G<\/jats:italic> has a pair of nontrivial nonisomorphic components then <jats:italic>RN(G)<\/jats:italic> \u2264 3. If <jats:italic>G<\/jats:italic> has a pair of nontrivial nonisomorphic components, is not a forest, and contains a nontrivial component other than <jats:italic>K<\/jats:italic><jats:sub>3<\/jats:sub> or <jats:italic>K<\/jats:italic><jats:sub>1,3<\/jats:sub> then <jats:italic>RN(G)<\/jats:italic> \u2264 2. Finally, if all nontrivial components of <jats:italic>G<\/jats:italic> are isomorphic to a graph with <jats:italic>k<\/jats:italic> edges, then <jats:italic>RN(G)<\/jats:italic> \u2264 <jats:italic>k<\/jats:italic> + 2. The edge reconstruction results in this paper are similar to the vertex reconstruction results stated by Myrvold (\u201cThe Ally\u2010Reconstruction Number of a Disconnected Graph,\u201d <jats:italic>Ars Combinatoria<\/jats:italic>, Vol. 28 [1989] pp. 123\u2010127), but a significant difference is that the edge reconstruction number of a disconnected graph is often two, while the vertex reconstruction number of a graph is always three or more. \u00a9 1995 John Wiley &amp; Sons, Inc.<\/jats:p>","DOI":"10.1002\/jgt.3190190310","type":"journal-article","created":{"date-parts":[[2007,5,26]],"date-time":"2007-05-26T13:54:12Z","timestamp":1180187652000},"page":"375-384","source":"Crossref","is-referenced-by-count":4,"title":["The edge reconstruction number of a disconnected graph"],"prefix":"10.1002","volume":"19","author":[{"given":"Robert","family":"Molina","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2006,10,6]]},"reference":[{"key":"e_1_2_1_2_2","doi-asserted-by":"publisher","DOI":"10.1002\/jgt.3190010306"},{"key":"e_1_2_1_3_2","doi-asserted-by":"publisher","DOI":"10.1002\/jgt.3190090403"},{"key":"e_1_2_1_4_2","unstructured":"R.Molina A correction of a proof on the reconstruction number of a disconnected graph.Ars Combinat.(1992). Submitted."},{"key":"e_1_2_1_5_2","first-page":"123","article-title":"The ally\u2010reconstruction number of a disconnected graph","volume":"28","author":"Myrvold W. J.","year":"1989","journal-title":"Ars Combinant."}],"container-title":["Journal of Graph Theory"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fjgt.3190190310","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/jgt.3190190310","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,10,26]],"date-time":"2023-10-26T20:58:02Z","timestamp":1698353882000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/jgt.3190190310"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1995,5]]},"references-count":4,"journal-issue":{"issue":"3","published-print":{"date-parts":[[1995,5]]}},"alternative-id":["10.1002\/jgt.3190190310"],"URL":"https:\/\/doi.org\/10.1002\/jgt.3190190310","archive":["Portico"],"relation":{},"ISSN":["0364-9024","1097-0118"],"issn-type":[{"value":"0364-9024","type":"print"},{"value":"1097-0118","type":"electronic"}],"subject":[],"published":{"date-parts":[[1995,5]]}}}