{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,6,22]],"date-time":"2024-06-22T20:36:25Z","timestamp":1719088585418},"reference-count":20,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2009,10,19]],"date-time":"2009-10-19T00:00:00Z","timestamp":1255910400000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Networks"],"published-print":{"date-parts":[[2010,8]]},"abstract":"Abstract<\/jats:title>An ({r<\/jats:italic>, r<\/jats:italic> + 1}; g<\/jats:italic>)\u2010cage is a graph with degree set {r<\/jats:italic>, r<\/jats:italic> + 1}, girth g<\/jats:italic>, and with the smallest possible order; every such graph is called a semiregular cage. In this article, semiregular cages are shown to be maximally edge\u2010connected and 2\u2010connected. As a consequence, ({3, 4}; g<\/jats:italic>)\u2010cages are proved to be maximally connected. \u00a9 2009 Wiley Periodicals, Inc. 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