{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T04:57:56Z","timestamp":1760245076639},"reference-count":7,"publisher":"Wiley","issue":"3","license":[{"start":{"date-parts":[[2006,10,11]],"date-time":"2006-10-11T00:00:00Z","timestamp":1160524800000},"content-version":"vor","delay-in-days":4028,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Networks"],"published-print":{"date-parts":[[1995,10]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>For given nonnegative integers <jats:italic>k<\/jats:italic> and <jats:italic>D<\/jats:italic>, we consider the problem of determining <jats:italic>n<\/jats:italic><jats:sub>0<\/jats:sub>(k, D), The smallest number <jats:italic>n<\/jats:italic> for which there exists a <jats:italic>k<\/jats:italic>\u2010regular bipartite graph on <jats:italic>n<\/jats:italic> vertices with diameter <jats:italic>D<\/jats:italic>. We solve the problem for all pairs <jats:italic>(k, D<\/jats:italic>) with <jats:italic>D<\/jats:italic> \u2262 2 (mod 4) and <jats:italic>D<\/jats:italic> \u2262 3 (mod 4), for all pairs (<jats:italic>k<\/jats:italic>, <jats:italic>D<\/jats:italic>) with <jats:italic>k<\/jats:italic> even or <jats:italic>k<\/jats:italic> prime and <jats:italic>D<\/jats:italic> \u2262 3 (mod 4), for all pairs with <jats:italic>D<\/jats:italic> \u2264 9 or <jats:italic>k<\/jats:italic> \u2264 4, and for a few other pairs. in the remaining cases, we obtain lower and upper bounds for n<jats:sub>0<\/jats:sub>(k, D).<\/jats:p>","DOI":"10.1002\/net.3230260303","type":"journal-article","created":{"date-parts":[[2007,5,12]],"date-time":"2007-05-12T20:21:41Z","timestamp":1179001301000},"page":"139-144","source":"Crossref","is-referenced-by-count":1,"title":["Bipartite regular graphs with fixed diameter"],"prefix":"10.1002","volume":"26","author":[{"given":"H. J.","family":"Broersma","sequence":"first","affiliation":[]},{"given":"F.","family":"G\u00f6bel","sequence":"additional","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2006,10,11]]},"reference":[{"key":"e_1_2_1_2_2","doi-asserted-by":"publisher","DOI":"10.1016\/0095-8956(84)90012-1"},{"key":"e_1_2_1_3_2","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-349-03521-2"},{"key":"e_1_2_1_4_2","first-page":"55","article-title":"The unique 4\u2010regular graphs on 14 and 15 vertices with diameter 2","volume":"25","author":"Broersma H. J.","year":"1988","journal-title":"Ars Comb."},{"key":"e_1_2_1_5_2","doi-asserted-by":"publisher","DOI":"10.1002\/jgt.3190090304"},{"key":"e_1_2_1_6_2","article-title":"Large planar graphs with given diameter and maximum degree","author":"Fellows M.","journal-title":"Disc. Appl. Math."},{"key":"e_1_2_1_7_2","unstructured":"M.Fellows P.HellandK.Seyffarth Constructions of dense planar networks. Submitted (preprint)."},{"key":"e_1_2_1_8_2","unstructured":"M. C.Heydemann Personal communication 11th British Combinational Conference London (1987)."}],"container-title":["Networks"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fnet.3230260303","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/net.3230260303","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,10,25]],"date-time":"2023-10-25T23:42:14Z","timestamp":1698277334000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/net.3230260303"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1995,10]]},"references-count":7,"journal-issue":{"issue":"3","published-print":{"date-parts":[[1995,10]]}},"alternative-id":["10.1002\/net.3230260303"],"URL":"https:\/\/doi.org\/10.1002\/net.3230260303","archive":["Portico"],"relation":{},"ISSN":["0028-3045","1097-0037"],"issn-type":[{"value":"0028-3045","type":"print"},{"value":"1097-0037","type":"electronic"}],"subject":[],"published":{"date-parts":[[1995,10]]}}}