{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,25]],"date-time":"2025-09-25T18:05:42Z","timestamp":1758823542494,"version":"3.41.2"},"reference-count":27,"publisher":"World Scientific Pub Co Pte Ltd","issue":"01n02","funder":[{"DOI":"10.13039\/501100001809","name":"The National Natural Science Foundation of China","doi-asserted-by":"crossref","award":["12101528"],"award-info":[{"award-number":["12101528"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"crossref"}]},{"name":"The Science and Technology Project of Xinjiang Uygur Autonomous Region","award":["2020D01C069"],"award-info":[{"award-number":["2020D01C069"]}]},{"name":"The Doctoral Startup Foundation of Xinjiang University","award":["62031224736"],"award-info":[{"award-number":["62031224736"]}]},{"name":"Tianchi Ph.D Program","award":["tcbs201905"],"award-info":[{"award-number":["tcbs201905"]}]},{"name":"National University Student Innovation Program Project","award":["202210755080"],"award-info":[{"award-number":["202210755080"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Parallel Process. Lett."],"published-print":{"date-parts":[[2023,3]]},"abstract":"<jats:p> An interconnection network can be modelled as a connected graph [Formula: see text]. The reliability of interconnection networks is critical for multiprocessor systems. Several conditional edge-connectivities have been introduced in the past for accurately reflecting various realistic network situations, with the [Formula: see text]-extra edge-connectivity being one such conditional edge-connectivity. The [Formula: see text]-extra edge-connectivity of [Formula: see text], denoted by [Formula: see text], is the minimum cardinality of faulty edges whose deletion disconnects the graph [Formula: see text] with each resulting component containing at least [Formula: see text] processors. In general, for a connected graph [Formula: see text], determining whether the graph exists an [Formula: see text]-extra edge-cut is [Formula: see text]-hard. The folded-crossed hypercube [Formula: see text] is a variation of the crossed hypercube [Formula: see text] with [Formula: see text] processors. In this paper, after excavating the layer structure of folded-crossed hypercube, we investigate some recursive properties of [Formula: see text], based on some recursive properties, an effective [Formula: see text] algorithm of [Formula: see text]-extra edge-connectivity of folded-crossed hypercube is designed, which can determine the exact value and the [Formula: see text]-optimality of [Formula: see text] for each positive integer [Formula: see text]. Our results solve this problem thoroughly. <\/jats:p>","DOI":"10.1142\/s0129626423500032","type":"journal-article","created":{"date-parts":[[2023,2,20]],"date-time":"2023-02-20T11:14:59Z","timestamp":1676891699000},"source":"Crossref","is-referenced-by-count":4,"title":["An <i>O<\/i>(log(<i>N<\/i>)) Algorithm View: Reliability Evaluation of Folded-crossed Hypercube in Terms of <i>h<\/i>-extra Edge-connectivity"],"prefix":"10.1142","volume":"33","author":[{"given":"Hengji","family":"Qiao","sequence":"first","affiliation":[{"name":"College of Mathematics and System Sciences, Xinjiang University, Urumqi, 830046, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Mingzu","family":"Zhang","sequence":"additional","affiliation":[{"name":"College of Mathematics and System Sciences, Xinjiang University, Urumqi, 830046, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Wenhuan","family":"Ma","sequence":"additional","affiliation":[{"name":"College of Mathematics and System Sciences, Xinjiang University, Urumqi, 830046, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xing","family":"Yang","sequence":"additional","affiliation":[{"name":"Department of Electrical and Computer Engineering, University of Mississippi, MS, 38677, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2023,2,21]]},"reference":[{"issue":"3","key":"S0129626423500032BIB001","doi-asserted-by":"crossref","first-page":"43","DOI":"10.5120\/807-1147","volume":"4","author":"Adhikari N.","year":"2010","journal-title":"International Journal of Computer Applications"},{"issue":"1","key":"S0129626423500032BIB002","doi-asserted-by":"crossref","first-page":"64","DOI":"10.1109\/71.824643","volume":"11","author":"Chang C.-P.","year":"2000","journal-title":"IEEE Transcation Parallel and Distributed Systems"},{"issue":"6","key":"S0129626423500032BIB003","doi-asserted-by":"crossref","first-page":"1594","DOI":"10.1109\/TC.2013.10","volume":"63","author":"Chang N.W.","year":"2014","journal-title":"IEEE Transcation Computers"},{"key":"S0129626423500032BIB004","doi-asserted-by":"crossref","first-page":"52","DOI":"10.1016\/j.ipl.2018.10.013","volume":"142","author":"Cai X.P.","year":"2019","journal-title":"Information Processing Letters"},{"issue":"1","key":"S0129626423500032BIB005","doi-asserted-by":"crossref","first-page":"31","DOI":"10.1109\/71.80187","volume":"2","author":"El-Amawy A.","year":"1991","journal-title":"IEEE Transcation on Parallel and Distributed Systems"},{"issue":"11","key":"S0129626423500032BIB006","doi-asserted-by":"crossref","first-page":"1312","DOI":"10.1109\/12.102840","volume":"40","author":"Efe K.","year":"1991","journal-title":"IEEE Transcation Computers"},{"issue":"5","key":"S0129626423500032BIB007","doi-asserted-by":"crossref","first-page":"513","DOI":"10.1109\/71.159036","volume":"3","author":"Efe K.","year":"1992","journal-title":"IEEE Transcation on Parallel and Distributed Systems"},{"key":"S0129626423500032BIB008","doi-asserted-by":"crossref","first-page":"49","DOI":"10.1016\/0012-365X(94)00369-T","volume":"155","author":"F\u00e0brega J.","year":"1996","journal-title":"Discrete Mathematics"},{"key":"S0129626423500032BIB009","doi-asserted-by":"publisher","DOI":"10.1142\/S0129054121500076"},{"key":"S0129626423500032BIB010","doi-asserted-by":"crossref","first-page":"726","DOI":"10.1007\/s00453-020-00772-w","volume":"83","author":"Ganian R.","year":"2021","journal-title":"Algorithmica"},{"key":"S0129626423500032BIB011","doi-asserted-by":"crossref","first-page":"1605","DOI":"10.1007\/s00453-020-00795-3","volume":"83","author":"Ganian R.","year":"2021","journal-title":"Algorithmica"},{"key":"S0129626423500032BIB012","doi-asserted-by":"crossref","first-page":"346","DOI":"10.1002\/net.3230130303","volume":"13","author":"Harary F.","year":"1983","journal-title":"Networks"},{"issue":"15","key":"S0129626423500032BIB013","doi-asserted-by":"crossref","first-page":"261","DOI":"10.1016\/j.dam.2020.04.030","volume":"285","author":"Lee C.W.","year":"2020","journal-title":"Discrete Applied Mathematics"},{"key":"S0129626423500032BIB014","doi-asserted-by":"crossref","first-page":"2753","DOI":"10.1016\/j.dam.2013.04.009","volume":"161","author":"Li H.","year":"2013","journal-title":"Discrete Applied Mathematics"},{"issue":"6","key":"S0129626423500032BIB015","doi-asserted-by":"crossref","first-page":"1086","DOI":"10.1109\/TDSC.2017.2726541","volume":"16","author":"Lin L.M.","year":"2017","journal-title":"IEEE Transactions on Dependable and Secure Computing"},{"issue":"1","key":"S0129626423500032BIB016","doi-asserted-by":"crossref","first-page":"183","DOI":"10.1016\/S0166-218X(00)00337-1","volume":"117","author":"Meng J.X.","year":"2002","journal-title":"Discrete Applied Mathematics"},{"issue":"1","key":"S0129626423500032BIB017","doi-asserted-by":"crossref","first-page":"31","DOI":"10.1016\/j.tcs.2016.12.006","volume":"662","author":"Montejano L.P.","year":"2017","journal-title":"Theoretical Computer Science"},{"key":"S0129626423500032BIB018","doi-asserted-by":"crossref","first-page":"146","DOI":"10.1007\/s00453-019-00608-2","volume":"82","author":"Prei\u00dfer J.E.","year":"2020","journal-title":"Algorithmica"},{"issue":"11","key":"S0129626423500032BIB019","doi-asserted-by":"crossref","first-page":"689","DOI":"10.1016\/j.ipl.2016.06.001","volume":"116","author":"Pai K.J.","year":"2016","journal-title":"Information Processing Letters"},{"issue":"1","key":"S0129626423500032BIB020","doi-asserted-by":"crossref","first-page":"96","DOI":"10.1016\/j.amc.2016.09.002","volume":"294","author":"Qiao Y.","year":"2017","journal-title":"Applied Mathematics and Computation"},{"key":"S0129626423500032BIB021","doi-asserted-by":"crossref","first-page":"101","DOI":"10.1007\/s11786-011-0085-2","volume":"5","author":"Rajasingh I.","year":"2011","journal-title":"Mathematics in Computer Science"},{"issue":"11","key":"S0129626423500032BIB022","doi-asserted-by":"crossref","first-page":"2117","DOI":"10.1109\/TPDS.2012.30","volume":"23","author":"Wang D.","year":"2012","journal-title":"IEEE Transactions on Parallel and Distributed Systems"},{"issue":"1","key":"S0129626423500032BIB023","doi-asserted-by":"crossref","first-page":"297","DOI":"10.1109\/TR.2017.2779130","volume":"67","author":"Zhang M.Z.","year":"2018","journal-title":"IEEE Transactions on Reliability"},{"key":"S0129626423500032BIB024","doi-asserted-by":"crossref","first-page":"71","DOI":"10.1016\/j.tcs.2015.11.049","volume":"615","author":"Zhang M.Z.","year":"2016","journal-title":"Theoretical Computer Science"},{"key":"S0129626423500032BIB025","doi-asserted-by":"crossref","first-page":"124","DOI":"10.1016\/j.jpdc.2020.08.009","volume":"147","author":"Zhang Q.F.","year":"2021","journal-title":"Journal of Parallel and Distributed Computing"},{"issue":"3","key":"S0129626423500032BIB026","doi-asserted-by":"crossref","first-page":"318","DOI":"10.1007\/s11227-008-0239-4","volume":"49","author":"Zhang Y.Q.","year":"2009","journal-title":"The Journal of Supercomputing"},{"issue":"11","key":"S0129626423500032BIB027","doi-asserted-by":"crossref","first-page":"917","DOI":"10.1016\/S1383-7621(02)00051-6","volume":"47","author":"Zhang Y.Q.","year":"2002","journal-title":"Journal of Systems Architecture"}],"container-title":["Parallel Processing Letters"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0129626423500032","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,5,26]],"date-time":"2023-05-26T06:42:37Z","timestamp":1685083357000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/10.1142\/S0129626423500032"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,2,21]]},"references-count":27,"journal-issue":{"issue":"01n02","published-print":{"date-parts":[[2023,3]]}},"alternative-id":["10.1142\/S0129626423500032"],"URL":"https:\/\/doi.org\/10.1142\/s0129626423500032","relation":{},"ISSN":["0129-6264","1793-642X"],"issn-type":[{"type":"print","value":"0129-6264"},{"type":"electronic","value":"1793-642X"}],"subject":[],"published":{"date-parts":[[2023,2,21]]},"article-number":"2350003"}}