{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,2]],"date-time":"2022-04-02T15:46:26Z","timestamp":1648914386799},"reference-count":8,"publisher":"World Scientific Pub Co Pte Lt","issue":"01n02","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. Inter. Net."],"published-print":{"date-parts":[[2011,3]]},"abstract":"<jats:p> Cayley digraphs of finite abelian groups are often used to model communication networks. Because of their applications, extremal Cayley digraphs have been studied extensively in recent years. Given any positive integers d and k. Let m<jats:sub>*<\/jats:sub>(d, k) denote the largest positive integer m such that there exists an m-element finite abelian group \u0393 and a k-element subset A of \u0393 such that diam ( Cay (\u0393, A)) \u2264 d, where diam ( Cay (\u0393, A)) denotes the diameter of the Cayley digraph Cay (\u0393, A) of \u0393 generated by A. Similarly, let m(d, k) denote the largest positive integer m such that there exists a k-element set A of integers with diam (\u2124<jats:sub>m<\/jats:sub>, A)) \u2264 d. In this paper, we prove, among other results, that [Formula: see text] for all d \u2265 1 and k \u2265 1. This means that the finite abelian group whose Cayley digraph is optimal with respect to its diameter and degree can be a cyclic group. <\/jats:p>","DOI":"10.1142\/s0219265911002873","type":"journal-article","created":{"date-parts":[[2011,12,12]],"date-time":"2011-12-12T12:07:10Z","timestamp":1323691630000},"page":"125-135","source":"Crossref","is-referenced-by-count":1,"title":["EXTREMAL CAYLEY DIGRAPHS OF FINITE ABELIAN GROUPS"],"prefix":"10.1142","volume":"12","author":[{"given":"ABBY GAIL","family":"MASK","sequence":"first","affiliation":[{"name":"Department of Mathematics, Texas State University, San Marcos, Texas 78666, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"JONI","family":"SCHNEIDER","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Texas State University, San Marcos, Texas 78666, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"XINGDE","family":"JIA","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Texas State University, San Marcos, Texas 78666, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2012,4,8]]},"reference":[{"key":"rf1","doi-asserted-by":"publisher","DOI":"10.1006\/jpdc.1995.1002"},{"key":"rf2","first-page":"257","volume":"23","author":"Bermond J. C.","journal-title":"Networks"},{"key":"rf3","doi-asserted-by":"publisher","DOI":"10.1137\/S0895480195286456"},{"key":"rf4","doi-asserted-by":"publisher","DOI":"10.1137\/S0895480190184811"},{"key":"rf6","doi-asserted-by":"publisher","DOI":"10.1137\/S0895480192242638"},{"key":"rf9","doi-asserted-by":"publisher","DOI":"10.1142\/S0129054197000203"},{"key":"rf11","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4757-3845-2"},{"key":"rf12","doi-asserted-by":"publisher","DOI":"10.1145\/321832.321838"}],"container-title":["Journal of Interconnection Networks"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0219265911002873","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,6]],"date-time":"2019-08-06T17:18:31Z","timestamp":1565111911000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0219265911002873"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2011,3]]},"references-count":8,"journal-issue":{"issue":"01n02","published-online":{"date-parts":[[2012,4,8]]},"published-print":{"date-parts":[[2011,3]]}},"alternative-id":["10.1142\/S0219265911002873"],"URL":"https:\/\/doi.org\/10.1142\/s0219265911002873","relation":{},"ISSN":["0219-2659","1793-6713"],"issn-type":[{"value":"0219-2659","type":"print"},{"value":"1793-6713","type":"electronic"}],"subject":[],"published":{"date-parts":[[2011,3]]}}}