{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,4,6]],"date-time":"2024-04-06T00:32:34Z","timestamp":1712363554687},"reference-count":17,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2006,2,6]],"date-time":"2006-02-06T00:00:00Z","timestamp":1139184000000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Journal of Graph Theory"],"published-print":{"date-parts":[[2006,5]]},"abstract":"Abstract<\/jats:title>For a connected graph the restricted edge\u2010connectivity \u03bb\u2032(G<\/jats:italic>) is defined as the minimum cardinality of an edge\u2010cut over all edge\u2010cuts S<\/jats:italic> such that there are no isolated vertices in G<\/jats:italic>\u2013S<\/jats:italic>. A graph G<\/jats:italic> is said to\nbe \u03bb\u2032\u2010optimal if \u03bb\u2032(G<\/jats:italic>)\u2009=\u2009\u03be(G<\/jats:italic>), where \u03be(G<\/jats:italic>) is the minimum edge\u2010degree in G<\/jats:italic> defined as \u03be(G<\/jats:italic>)\u2009=\u2009min<\/jats:italic>{d<\/jats:italic>(u<\/jats:italic>)\u2009+\u2009d<\/jats:italic>(v<\/jats:italic>)\u2009\u2212\u20092:uv<\/jats:italic> \u2208 E<\/jats:italic>(G<\/jats:italic>)}, d<\/jats:italic>(u<\/jats:italic>) denoting the degree of a vertex u<\/jats:italic>. A. Hellwig and L. Volkmann [Sufficient conditions for \u03bb\u2032\u2010optimality in graphs of diameter 2, Discrete Math 283 (2004), 113\u2013120] gave a sufficient condition for \u03bb\u2032\u2010optimality in graphs of diameter 2. In this paper, we generalize this condition in graphs of diameter g<\/jats:italic>\u2009\u2212\u20091, g<\/jats:italic> being the girth of the graph, and show that a graph G<\/jats:italic> with diameter at most g<\/jats:italic>\u2009\u2212\u20092 is \u03bb\u2032\u2010optimal. \u00a9 2006 Wiley Periodicals, Inc. 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