{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,10,23]],"date-time":"2023-10-23T19:40:41Z","timestamp":1698090041144},"reference-count":4,"publisher":"Wiley","issue":"4","license":[{"start":{"date-parts":[[2006,10,5]],"date-time":"2006-10-05T00:00:00Z","timestamp":1160006400000},"content-version":"vor","delay-in-days":5147,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Journal of Graph Theory"],"published-print":{"date-parts":[[1992,9]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>Whitney's theorem on 2\u2010isomorphism characterizes the set of graphs having the same cycles as a given graph, where a cycle is regarded as a set of edges. In this paper, <jats:italic>vertex 2\u2010isomorphism<\/jats:italic> is defined and used to prove a vertex analogue of Whitney's theorem. The main theorem states that two connected graphs have the same set of cycles, where a cycle is now regarded as a set of vertices, if and only if one can be obtained from the other by a sequence of simple operations. \u00a9 1992 John Wiley &amp; Sons, Inc.<\/jats:p>","DOI":"10.1002\/jgt.3190160407","type":"journal-article","created":{"date-parts":[[2007,6,8]],"date-time":"2007-06-08T06:53:41Z","timestamp":1181285621000},"page":"335-347","source":"Crossref","is-referenced-by-count":2,"title":["Vertex 2\u2010isomorphism"],"prefix":"10.1002","volume":"16","author":[{"given":"R.","family":"Swaminathan","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Donald K.","family":"Wagner","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2006,10,5]]},"reference":[{"key":"e_1_2_1_2_2","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-349-03521-2"},{"key":"e_1_2_1_3_2","volume-title":"Combinatorial Problems and Exercises","author":"Lov\u00e1sz L.","year":"1979"},{"key":"e_1_2_1_4_2","doi-asserted-by":"publisher","DOI":"10.4064\/fm-10-1-96-115"},{"key":"e_1_2_1_5_2","doi-asserted-by":"publisher","DOI":"10.2307\/2371127"}],"container-title":["Journal of Graph Theory"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fjgt.3190160407","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/jgt.3190160407","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,10,23]],"date-time":"2023-10-23T19:07:52Z","timestamp":1698088072000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/jgt.3190160407"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1992,9]]},"references-count":4,"journal-issue":{"issue":"4","published-print":{"date-parts":[[1992,9]]}},"alternative-id":["10.1002\/jgt.3190160407"],"URL":"https:\/\/doi.org\/10.1002\/jgt.3190160407","archive":["Portico"],"relation":{},"ISSN":["0364-9024","1097-0118"],"issn-type":[{"value":"0364-9024","type":"print"},{"value":"1097-0118","type":"electronic"}],"subject":[],"published":{"date-parts":[[1992,9]]}}}