{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,3,29]],"date-time":"2022-03-29T07:39:55Z","timestamp":1648539595689},"reference-count":7,"publisher":"World Scientific Pub Co Pte Lt","issue":"02","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Discrete Math. Algorithm. Appl."],"published-print":{"date-parts":[[2010,6]]},"abstract":"<jats:p> The super edge-connectivity \u03bb\u2032 of a connected graph G is the minimum cardinality of an edge-cut F in G such that every component of G\u2013F contains at least two vertices. Let two connected graphs G<jats:sub>m<\/jats:sub> and G<jats:sub>p<\/jats:sub> have m and p vertices, minimum degree \u03b4(G<jats:sub>m<\/jats:sub>) and \u03b4(G<jats:sub>p<\/jats:sub>), edge-connectivity \u03bb(G<jats:sub>m<\/jats:sub>) and \u03bb(G<jats:sub>p<\/jats:sub>), respectively. This paper shows that min {p\u03bb(G<jats:sub>m<\/jats:sub>), \u03bb(G<jats:sub>p<\/jats:sub>) + \u03b4(G<jats:sub>m<\/jats:sub>), \u03b4(G<jats:sub>m<\/jats:sub>)(\u03bb(G<jats:sub>p<\/jats:sub>) + 1), (\u03b4(G<jats:sub>m<\/jats:sub>) + 1)\u03bb(G<jats:sub>p<\/jats:sub>)} \u2264 \u03bb(G<jats:sub>m<\/jats:sub> * G<jats:sub>p<\/jats:sub>) \u2264 \u03b4(G<jats:sub>m<\/jats:sub>) + \u03b4(G<jats:sub>p<\/jats:sub>), where the product graph G<jats:sub>m<\/jats:sub> * G<jats:sub>p<\/jats:sub> of two given graphs G<jats:sub>m<\/jats:sub> and G<jats:sub>p<\/jats:sub>, defined by J. C. Bermond et al. [J. Combin. Theory B36 (1984) 32\u201348] in the context of the so-called (\u25b3, D)-problem, is one interesting model in the design of large reliable networks. Moreover, this paper determines \u03bb\u2032(G<jats:sub>m<\/jats:sub> * G<jats:sub>p<\/jats:sub>) \u2264 min {p\u03b4(G<jats:sub>m<\/jats:sub>), \u03be(G<jats:sub>p<\/jats:sub>) + 2\u03b4(G<jats:sub>m<\/jats:sub>)} and \u03bb\u2032(G<jats:sub>1<\/jats:sub> \u2295 G<jats:sub>2<\/jats:sub>) \u2265 min {n, \u03bb<jats:sub>1<\/jats:sub> + \u03bb<jats:sub>2<\/jats:sub>} if \u03b4<jats:sub>1<\/jats:sub> = \u03b4<jats:sub>2<\/jats:sub>. <\/jats:p>","DOI":"10.1142\/s179383091000053x","type":"journal-article","created":{"date-parts":[[2010,7,5]],"date-time":"2010-07-05T10:31:23Z","timestamp":1278325883000},"page":"143-150","source":"Crossref","is-referenced-by-count":0,"title":["ON EDGE-CONNECTIVITY AND SUPER EDGE-CONNECTIVITY OF INTERCONNECTION NETWORKS MODELED BY PRODUCT GRAPHS"],"prefix":"10.1142","volume":"02","author":[{"given":"CHUNXIANG","family":"WANG","sequence":"first","affiliation":[{"name":"School of Mathematics and Statistics, Huazhong Normal University, Wuhan, 430079, P. R. China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2012,4,5]]},"reference":[{"key":"rf1","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-349-03521-2"},{"key":"rf2","first-page":"253","volume":"29","author":"Fiol M. A.","journal-title":"Ars Combin. B"},{"key":"rf3","doi-asserted-by":"publisher","DOI":"10.1016\/0020-0190(88)90025-7"},{"key":"rf4","doi-asserted-by":"publisher","DOI":"10.1002\/net.20149"},{"key":"rf5","doi-asserted-by":"publisher","DOI":"10.1016\/0095-8956(84)90012-1"},{"key":"rf6","doi-asserted-by":"publisher","DOI":"10.1002\/jgt.20053"},{"key":"rf7","doi-asserted-by":"publisher","DOI":"10.1016\/S0012-365X(01)00232-1"}],"container-title":["Discrete Mathematics, Algorithms and Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S179383091000053X","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,7]],"date-time":"2019-08-07T01:20:34Z","timestamp":1565140834000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S179383091000053X"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2010,6]]},"references-count":7,"journal-issue":{"issue":"02","published-online":{"date-parts":[[2012,4,5]]},"published-print":{"date-parts":[[2010,6]]}},"alternative-id":["10.1142\/S179383091000053X"],"URL":"https:\/\/doi.org\/10.1142\/s179383091000053x","relation":{},"ISSN":["1793-8309","1793-8317"],"issn-type":[{"value":"1793-8309","type":"print"},{"value":"1793-8317","type":"electronic"}],"subject":[],"published":{"date-parts":[[2010,6]]}}}