{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,4]],"date-time":"2022-04-04T04:24:07Z","timestamp":1649046247856},"reference-count":14,"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":[[2008,3]]},"abstract":"<jats:p> Let \u0393 be a finite group with a nonempty subset A. The Cayley graph Cay (\u0393, A) of \u0393 generated by A is defined as the digraph with vertex set \u0393 and edge set {(x,y) | x<jats:sup>-1<\/jats:sup> y \u2208 A}. Cay (\u0393, A) can be regarded as an undirected graph if x<jats:sup>-1<\/jats:sup> \u2208 A for all x \u2208 A. Let [Formula: see text] denote the largest integer M so that there exists a set of integers A = {\u00b11, \u00b1a<jats:sub>2<\/jats:sub>;\u2026, \u00b1a<jats:sub>k<\/jats:sub>} such that the average distance between all pairs of vertices of Cay (\u2124<jats:sub>M<\/jats:sub>,A) is at most r, where \u2124<jats:sub>M<\/jats:sub> is the additive group of residue classes modulo M. It is proved in this paper that [Formula: see text] It is also proved that [Formula: see text] <\/jats:p>","DOI":"10.1142\/s0219265908002163","type":"journal-article","created":{"date-parts":[[2008,9,1]],"date-time":"2008-09-01T01:51:53Z","timestamp":1220233913000},"page":"73-82","source":"Crossref","is-referenced-by-count":0,"title":["EXTREMAL CAYLEY GRAPHS OF FINITE CYCLIC GROUPS"],"prefix":"10.1142","volume":"09","author":[{"given":"JOSEPH J.","family":"LEE","sequence":"first","affiliation":[{"name":"Harvard School of Engineering and Applied Sciences, Harvard University, 29 Oxford St. Cambridge, MA 02138, USA"}]},{"given":"ELYSIA J.","family":"SHEU","sequence":"additional","affiliation":[{"name":"Sibley School of Mechanical and Aerospace Engineering, Cornell University, 105 Upson Hall, Ithaca, NY 14853, USA"}]},{"given":"XINGDE","family":"JIA","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Texas State University, San Marcos, TX 78666, USA"}]}],"member":"219","published-online":{"date-parts":[[2011,11,21]]},"reference":[{"key":"rf2","doi-asserted-by":"publisher","DOI":"10.1016\/S0195-6698(89)80067-8"},{"key":"rf3","doi-asserted-by":"publisher","DOI":"10.1006\/jpdc.1995.1002"},{"key":"rf4","doi-asserted-by":"publisher","DOI":"10.1002\/net.3230230407"},{"key":"rf5","doi-asserted-by":"publisher","DOI":"10.1137\/0601045"},{"key":"rf6","doi-asserted-by":"crossref","DOI":"10.1201\/9781315214733","volume-title":"Parallel System Interconnections and Communications","author":"Grammatikakis M. D.","year":"2000"},{"key":"rf7","series-title":"Discrete Mathematics and its Applications (Boca Raton)","volume-title":"Graph theory and its applications","author":"Gross J. L.","year":"2006"},{"key":"rf8","doi-asserted-by":"publisher","DOI":"10.1016\/S0304-3975(01)00341-3"},{"key":"rf9","doi-asserted-by":"publisher","DOI":"10.1137\/S0895480190184811"},{"key":"rf10","first-page":"61","volume":"66","author":"Hsu D. F.","journal-title":"Utilitas Math."},{"key":"rf12","unstructured":"D. F.\u00a0Hsu and J.\u00a0Shapiro, Graph theory, combinatorics, algorithms, and applications (San Francisco, CA, 1989) (SIAM, Philadelphia, PA, 1991)\u00a0pp. 254\u2013265."},{"key":"rf13","first-page":"55","volume":"16","author":"Hsu D. F.","journal-title":"J. Combin. Inform. System Sci."},{"key":"rf14","doi-asserted-by":"publisher","DOI":"10.1016\/0022-314X(92)90088-7"},{"key":"rf16","doi-asserted-by":"publisher","DOI":"10.1016\/j.disc.2004.07.036"},{"key":"rf17","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\/S0219265908002163","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,7]],"date-time":"2019-08-07T18:00:43Z","timestamp":1565200843000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0219265908002163"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2008,3]]},"references-count":14,"journal-issue":{"issue":"01n02","published-online":{"date-parts":[[2011,11,21]]},"published-print":{"date-parts":[[2008,3]]}},"alternative-id":["10.1142\/S0219265908002163"],"URL":"https:\/\/doi.org\/10.1142\/s0219265908002163","relation":{},"ISSN":["0219-2659","1793-6713"],"issn-type":[{"value":"0219-2659","type":"print"},{"value":"1793-6713","type":"electronic"}],"subject":[],"published":{"date-parts":[[2008,3]]}}}