{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,11,16]],"date-time":"2023-11-16T23:21:36Z","timestamp":1700176896289},"reference-count":4,"publisher":"Wiley","issue":"3","license":[{"start":{"date-parts":[[2006,10,3]],"date-time":"2006-10-03T00:00:00Z","timestamp":1159833600000},"content-version":"vor","delay-in-days":9894,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Journal of Graph Theory"],"published-print":{"date-parts":[[1979,9]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>Let <jats:italic>G<\/jats:italic> be a connected graph of order <jats:italic>p<\/jats:italic> \u2265 2, with edge\u2010connectivity \u03ba<jats:sub>1<\/jats:sub>(<jats:italic>G<\/jats:italic>) and minimum degree \u03b4(<jats:italic>G<\/jats:italic>). It is shown her ethat in order to obtain the equality \u03ba<jats:sub>1<\/jats:sub>(<jats:italic>G<\/jats:italic>) = \u03b4(<jats:italic>G<\/jats:italic>), it is sufficient that, for each vertex <jats:italic>x<\/jats:italic> of minimum degree in <jats:italic>G<\/jats:italic>, the vertices in the neighbourhood <jats:italic>N<\/jats:italic>(<jats:italic>x<\/jats:italic>) of <jats:italic>x<\/jats:italic> have sufficiently large degree sum. This result implies a previous result of Chartrand, which required that \u03b4(<jats:italic>G<\/jats:italic>) \u2265 [<jats:italic>p<\/jats:italic>\/2].<\/jats:p>","DOI":"10.1002\/jgt.3190030307","type":"journal-article","created":{"date-parts":[[2007,5,26]],"date-time":"2007-05-26T10:24:59Z","timestamp":1180175099000},"page":"251-255","source":"Crossref","is-referenced-by-count":10,"title":["A sufficient condition for equality of edge\u2010connectivity and minimum degree of a graph"],"prefix":"10.1002","volume":"3","author":[{"given":"Donald L.","family":"Goldsmith","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Roger C.","family":"Entringer","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2006,10,3]]},"reference":[{"key":"e_1_2_1_2_2","doi-asserted-by":"publisher","DOI":"10.1137\/0114065"},{"key":"e_1_2_1_3_2","doi-asserted-by":"publisher","DOI":"10.1016\/0012-365X(78)90184-X"},{"key":"e_1_2_1_4_2","doi-asserted-by":"publisher","DOI":"10.1016\/0012-365X(74)90154-X"},{"key":"e_1_2_1_5_2","first-page":"71","article-title":"Critical graphs of given diameter","volume":"30","author":"Plesnik J.","year":"1975","journal-title":"Acta Fac. Rerum Natur. Univ. Comenian Math."}],"container-title":["Journal of Graph Theory"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fjgt.3190030307","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/jgt.3190030307","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,10,19]],"date-time":"2023-10-19T13:12:55Z","timestamp":1697721175000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/jgt.3190030307"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1979,9]]},"references-count":4,"journal-issue":{"issue":"3","published-print":{"date-parts":[[1979,9]]}},"alternative-id":["10.1002\/jgt.3190030307"],"URL":"https:\/\/doi.org\/10.1002\/jgt.3190030307","archive":["Portico"],"relation":{},"ISSN":["0364-9024","1097-0118"],"issn-type":[{"value":"0364-9024","type":"print"},{"value":"1097-0118","type":"electronic"}],"subject":[],"published":{"date-parts":[[1979,9]]}}}