{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,1]],"date-time":"2026-02-01T19:52:12Z","timestamp":1769975532164,"version":"3.49.0"},"reference-count":3,"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":7429,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Journal of Graph Theory"],"published-print":{"date-parts":[[1986,6]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>A nontrivial connected graph <jats:italic>G<\/jats:italic> is called even if for each vertex <jats:italic>v<\/jats:italic> of <jats:italic>G<\/jats:italic> there is a unique vertex <jats:styled-content><jats:italic>v<\/jats:italic><\/jats:styled-content> such that <jats:italic>d<\/jats:italic>(<jats:italic>v<\/jats:italic>, <jats:styled-content><jats:italic>v<\/jats:italic><\/jats:styled-content>) = diam <jats:italic>G.<\/jats:italic> Special classes of even graphs are defined and compared to each other. In particular, an even graph <jats:italic>G<\/jats:italic> is called symmetric if <jats:italic>d<\/jats:italic>(<jats:italic>u<\/jats:italic>, <jats:italic>v<\/jats:italic>) + <jats:italic>d<\/jats:italic>(<jats:italic>u<\/jats:italic>, <jats:styled-content>v<\/jats:styled-content>) = diam <jats:italic>G<\/jats:italic> for all <jats:italic>u<\/jats:italic>, <jats:italic>v<\/jats:italic> \u2208 <jats:italic>V<\/jats:italic>(<jats:italic>G<\/jats:italic>). Several properties of even and symmetric even graphs are stated. For an even graph of order <jats:italic>n<\/jats:italic> and diameter <jats:italic>d<\/jats:italic> other than an even cycle it is shown that <jats:italic>n<\/jats:italic> \u2265 3<jats:italic>d<\/jats:italic> \u2013 1 and conjectured that <jats:italic>n<\/jats:italic> \u2265 4<jats:italic>d<\/jats:italic> \u2013 4. This conjecture is proved for symmetric even graphs and it is shown that for each pair of integers <jats:italic>n, d<\/jats:italic> with <jats:italic>n<\/jats:italic> even, <jats:italic>d<\/jats:italic> \u2265 2 and <jats:italic>n<\/jats:italic> \u2265 4<jats:italic>d<\/jats:italic> \u2013 4 there exists an even graph of order <jats:italic>n<\/jats:italic> and diameter <jats:italic>d<\/jats:italic>. Several ways of constructing new even graphs from known ones are presented.<\/jats:p>","DOI":"10.1002\/jgt.3190100212","type":"journal-article","created":{"date-parts":[[2007,5,26]],"date-time":"2007-05-26T11:55:31Z","timestamp":1180180531000},"page":"225-239","source":"Crossref","is-referenced-by-count":19,"title":["Even graphs"],"prefix":"10.1002","volume":"10","author":[{"given":"F.","family":"G\u00f6bel","sequence":"first","affiliation":[]},{"given":"H. J.","family":"Veldman","sequence":"additional","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2006,10,3]]},"reference":[{"key":"e_1_2_1_2_2","volume-title":"Graphs and Digraphs","author":"Behzad M.","year":"1979"},{"key":"e_1_2_1_3_2","doi-asserted-by":"publisher","DOI":"10.1002\/jgt.3190040112"},{"key":"e_1_2_1_4_2","doi-asserted-by":"publisher","DOI":"10.1016\/0012-365X(83)90271-6"}],"container-title":["Journal of Graph Theory"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fjgt.3190100212","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/jgt.3190100212","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,10,21]],"date-time":"2023-10-21T22:53:01Z","timestamp":1697928781000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/jgt.3190100212"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1986,6]]},"references-count":3,"journal-issue":{"issue":"2","published-print":{"date-parts":[[1986,6]]}},"alternative-id":["10.1002\/jgt.3190100212"],"URL":"https:\/\/doi.org\/10.1002\/jgt.3190100212","archive":["Portico"],"relation":{},"ISSN":["0364-9024","1097-0118"],"issn-type":[{"value":"0364-9024","type":"print"},{"value":"1097-0118","type":"electronic"}],"subject":[],"published":{"date-parts":[[1986,6]]}}}