{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,1]],"date-time":"2026-04-01T09:46:44Z","timestamp":1775036804317,"version":"3.50.1"},"reference-count":27,"publisher":"Oxford University Press (OUP)","issue":"9","license":[{"start":{"date-parts":[[2019,11,13]],"date-time":"2019-11-13T00:00:00Z","timestamp":1573603200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/academic.oup.com\/journals\/pages\/open_access\/funder_policies\/chorus\/standard_publication_model"}],"funder":[{"DOI":"10.13039\/100007834","name":"Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61702100"],"award-info":[{"award-number":["61702100"]}],"id":[{"id":"10.13039\/100007834","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100007834","name":"Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61972093"],"award-info":[{"award-number":["61972093"]}],"id":[{"id":"10.13039\/100007834","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100007834","name":"Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61702103"],"award-info":[{"award-number":["61702103"]}],"id":[{"id":"10.13039\/100007834","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100007834","name":"Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61771140"],"award-info":[{"award-number":["61771140"]}],"id":[{"id":"10.13039\/100007834","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100002858","name":"China Postdoctoral Science Foundation","doi-asserted-by":"publisher","award":["2018T110636"],"award-info":[{"award-number":["2018T110636"]}],"id":[{"id":"10.13039\/501100002858","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100002858","name":"China Postdoctoral Science Foundation","doi-asserted-by":"publisher","award":["2017M612107"],"award-info":[{"award-number":["2017M612107"]}],"id":[{"id":"10.13039\/501100002858","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Foundation of Digital Fujian Institute of Big Data for Agriculture and Forestry","award":["117-KJG18019A"],"award-info":[{"award-number":["117-KJG18019A"]}]},{"DOI":"10.13039\/501100008462","name":"Fujian University of Technology","doi-asserted-by":"publisher","award":["G-Z17008"],"award-info":[{"award-number":["G-Z17008"]}],"id":[{"id":"10.13039\/501100008462","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Education Department of Fujian Province","award":["JAT170397"],"award-info":[{"award-number":["JAT170397"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2020,8,20]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>The connectivity of a graph is a classic measure for fault tolerance of the network. Restricted connectivity measure is a crucial subject for a multiprocessor system\u2019s ability to tolerate fault processors, and improves the connectivity measurement accuracy. Furthermore, if a network possesses a restricted connectivity property, it is more reliable with a lower vertex failure rate compared with other networks. The $\\left (n,k\\right )$-dimensional enhanced hypercube, denoted by $Q_{n,k}$, a variant of hypercube, which is a well-known interconnection network. In this paper, we analyze the fault tolerant properties for $\\left (n,k\\right )$-enhanced hypercube, and establish the $1$-restricted connectivity of $Q_{n,k} (n\\ge k+1)$ and $\\{2,3\\}$-restricted connectivity of $(n,k)$-enhanced hypercube $Q_{n,k} (n=k+1)$. Furthermore, we propose the tight upper bound of $\\{2,3\\}$-restricted connectivity of $Q_{n,k} (n&amp;gt; k+1)$. Moreover, we show many figures to better illustrate the process of the proofs.<\/jats:p>","DOI":"10.1093\/comjnl\/bxz071","type":"journal-article","created":{"date-parts":[[2019,8,1]],"date-time":"2019-08-01T11:10:17Z","timestamp":1564657817000},"page":"1355-1371","source":"Crossref","is-referenced-by-count":9,"title":["{1,2,3}-Restricted Connectivity of $(n,k)$-Enhanced Hypercubes"],"prefix":"10.1093","volume":"63","author":[{"given":"Hui","family":"Yu","sequence":"first","affiliation":[{"name":"Faculty of Computer and Information Sciences, Digital Fujian Institute of Big Data for Agriculture and Forestry, Fujian Agriculture and Forestry University, Fuzhou, Fujian 350002, P.R. China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jiejie","family":"Yang","sequence":"additional","affiliation":[{"name":"College of Physics and Information Engineering, Fuzhou University, Fuzhou, Fujian 350116, P.R. China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Limei","family":"Lin","sequence":"additional","affiliation":[{"name":"Faculty of Computer and Information Sciences, Digital Fujian Institute of Big Data for Agriculture and Forestry, Fujian Agriculture and Forestry University, Fuzhou, Fujian 350002, P.R. China"},{"name":"Collage of Mathematics and Informatics, Fujian Normal University, Fuzhou, Fujian 350117, P.R. China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yanze","family":"Huang","sequence":"additional","affiliation":[{"name":"School of Mathematics and Physics, Fujian Provincial Key Laboratory of Big Data Mining and Applications, Fujian University of Technology, Fuzhou, Fujian 350118, P.R. China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jine","family":"Li","sequence":"additional","affiliation":[{"name":"Faculty of Computer and Information Sciences, Digital Fujian Institute of Big Data for Agriculture and Forestry, Fujian Agriculture and Forestry University, Fuzhou, Fujian 350002, P.R. China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Riqing","family":"Chen","sequence":"additional","affiliation":[{"name":"Faculty of Computer and Information Sciences, Digital Fujian Institute of Big Data for Agriculture and Forestry, Fujian Agriculture and Forestry University, Fuzhou, Fujian 350002, P.R. China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"286","published-online":{"date-parts":[[2019,11,13]]},"reference":[{"key":"2020091506341137700_ref1","doi-asserted-by":"crossref","first-page":"22","DOI":"10.1109\/TCC.2013.2","article-title":"A tabu search algorithm for the location of data centers and software components in green cloud computing networks","volume":"1","author":"Larumbe","year":"2013","journal-title":"IEEE Trans. Cloud Comput."},{"key":"2020091506341137700_ref2","doi-asserted-by":"crossref","first-page":"175","DOI":"10.1016\/j.physrep.2005.10.009","article-title":"Complex networks: structure and dynamics","volume":"424","author":"Boccaletti","year":"2006","journal-title":"Physical Reports"},{"key":"2020091506341137700_ref3","doi-asserted-by":"crossref","first-page":"34","DOI":"10.1016\/j.ins.2016.05.048","article-title":"Trustworthiness-hypercube-based reliable communication in mobile social networks","volume":"369","author":"Lin","year":"2016","journal-title":"Inform. Sci."},{"key":"2020091506341137700_ref4","first-page":"1368","article-title":"Social feature-based multi-path routing in delay tolerant networks","volume-title":"IEEE INFOCOM Conf.","author":"Wu","year":"2012"},{"key":"2020091506341137700_ref5","doi-asserted-by":"crossref","first-page":"383","DOI":"10.1109\/TC.2012.209","article-title":"Hypercube-based multipath social feature routing in human contact networks","volume":"63","author":"Wu","year":"2014","journal-title":"IEEE Trans. Comput."},{"key":"2020091506341137700_ref6","doi-asserted-by":"crossref","first-page":"284","DOI":"10.1109\/12.76405","article-title":"Enhanced hypercubes","volume":"40","author":"Tzeng","year":"1991","journal-title":"IEEE Trans. Comput."},{"key":"2020091506341137700_ref7","doi-asserted-by":"crossref","first-page":"60","DOI":"10.1016\/j.tcs.2017.07.005","article-title":"The vulnerability of the diameter of the enhanced hypercubes","volume":"694","author":"Ma","year":"2017","journal-title":"Theor. Comput. Sci."},{"key":"2020091506341137700_ref8","doi-asserted-by":"crossref","first-page":"1054","DOI":"10.1109\/12.312114","article-title":"Diagnosability of enhanced hypercubes","volume":"43","author":"Wang","year":"1994","journal-title":"IEEE Trans. Comput."},{"key":"2020091506341137700_ref9","doi-asserted-by":"crossref","first-page":"266","DOI":"10.1002\/net.20002","article-title":"Complete binary trees in folded and enhanced cubes","volume":"43","author":"Choudum","year":"2004","journal-title":"Networks - Bognor Regis"},{"key":"2020091506341137700_ref10","doi-asserted-by":"crossref","first-page":"3157","DOI":"10.1109\/TC.2015.2512866","article-title":"The t\/k-diagnosability for regular networks","volume":"65","author":"Lin","year":"2016","journal-title":"IEEE Trans. Comput."},{"key":"2020091506341137700_ref11","first-page":"121","article-title":"Extraconnectivity of folded hypercubes","volume":"116","author":"Yang","year":"2014","journal-title":"Ars Combin."},{"key":"2020091506341137700_ref12","doi-asserted-by":"crossref","first-page":"218","DOI":"10.1109\/12.262126","article-title":"Conditional connectivity measures for large multiprocessor systems","volume":"43","author":"Latifi","year":"1994","journal-title":"IEEE Trans. Comput."},{"key":"2020091506341137700_ref13","doi-asserted-by":"crossref","first-page":"1586","DOI":"10.1109\/12.42131","article-title":"Generalized measures of fault tolerance with application to n-cube networks","volume":"38","author":"Esfahanian","year":"1989","journal-title":"IEEE Trans. Comput."},{"key":"2020091506341137700_ref14","doi-asserted-by":"crossref","first-page":"1335","DOI":"10.1016\/j.aml.2011.11.040","article-title":"Generalized measures of fault tolerance in hypercube networks","volume":"25","author":"Yang","year":"2012","journal-title":"Appl. Math. Lett."},{"key":"2020091506341137700_ref15","doi-asserted-by":"crossref","first-page":"1165","DOI":"10.1109\/TPDS.2014.2318305","article-title":"The g-good-neighbor conditional diagnosability of k-ary n-cubes under the PMC modeland MM* model","volume":"26","author":"Yuan","year":"2015","journal-title":"IEEE Trans. Parall. Distr. Syst."},{"key":"2020091506341137700_ref16","doi-asserted-by":"crossref","first-page":"533","DOI":"10.1016\/j.ipl.2013.04.007","article-title":"Generalized measures of fault tolerance in exchanged hypercubes","volume":"113","author":"Li","year":"2013","journal-title":"Inform. Process. Lett."},{"key":"2020091506341137700_ref17","doi-asserted-by":"crossref","first-page":"1007","DOI":"10.1016\/j.ipl.2010.08.015","article-title":"A kind of conditional fault tolerance of (n, k)-star graphs","volume":"110","author":"Yang","year":"2010","journal-title":"Inform. Process. Lett."},{"key":"2020091506341137700_ref18","doi-asserted-by":"crossref","first-page":"533","DOI":"10.1109\/TPDS.2015.2400459","article-title":"The extra, restricted connectivity and conditional diagnosability of split-star networks","volume":"27","author":"Lin","year":"2016","journal-title":"IEEE Trans. Parall. Distr. Syst."},{"key":"2020091506341137700_ref19","doi-asserted-by":"crossref","first-page":"78","DOI":"10.1016\/j.tcs.2015.11.050","article-title":"2, 3-restricted connectivity of locally twisted cubes","volume":"615","author":"Hsieh","year":"2016","journal-title":"Theor. Comput. Sci."},{"key":"2020091506341137700_ref20","doi-asserted-by":"crossref","first-page":"330","DOI":"10.1016\/j.dam.2016.08.012","article-title":"H-restricted connectivity of locally twisted cubes","volume":"217","author":"Wei","year":"2017","journal-title":"Discrete Appl. Math."},{"key":"2020091506341137700_ref21","doi-asserted-by":"crossref","first-page":"66","DOI":"10.1007\/s11227-008-0206-0","article-title":"The super spanning connectivity and super spanning laceability of the enhanced hypercubes","volume":"48","author":"Chang","year":"2009","journal-title":"J. Supercomput."},{"key":"2020091506341137700_ref22","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4757-3387-7","volume-title":"Topological Structure and Analysis of Interconnection Networks","author":"Xu","year":"2001"},{"key":"2020091506341137700_ref23","doi-asserted-by":"crossref","first-page":"285","DOI":"10.1109\/TR.2017.2760905","article-title":"The relationship between g-restricted connectivity and g-good-neighbor fault diagnosability of general regular networks","volume":"67","author":"Lin","year":"2018","journal-title":"IEEE Trans. Reliab."},{"key":"2020091506341137700_ref24","doi-asserted-by":"crossref","first-page":"1369","DOI":"10.1109\/12.817401","article-title":"Diagnosability of hypercubes and enhanced hypercubes under the comparison diagnosis model","volume":"48","author":"Wang","year":"1999","journal-title":"IEEE Trans. Comput."},{"key":"2020091506341137700_ref25","first-page":"251","article-title":"Properties of enhanced hypercube networks","volume":"3","author":"Liu","year":"2008","journal-title":"J. Syst. Sci. Inform."},{"key":"2020091506341137700_ref26","doi-asserted-by":"crossref","first-page":"669","DOI":"10.1016\/j.jcss.2013.01.013","article-title":"2,3-extraconnectivities of hypercube-like networks","volume":"79","author":"Chang","year":"2013","journal-title":"J. Comput. Syst. Sci."},{"key":"2020091506341137700_ref27","doi-asserted-by":"crossref","first-page":"287","DOI":"10.1007\/s12021-012-9146-1","article-title":"The connection-set algebra\u2014a novel formalism for the representation of connectivity structure in neuronal network models","volume":"10","author":"Djurfeldt","year":"2012","journal-title":"Neuroinformatics"}],"container-title":["The Computer Journal"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/academic.oup.com\/comjnl\/article-pdf\/63\/9\/1355\/33747689\/bxz071.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"http:\/\/academic.oup.com\/comjnl\/article-pdf\/63\/9\/1355\/33747689\/bxz071.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,9,15]],"date-time":"2020-09-15T10:36:24Z","timestamp":1600166184000},"score":1,"resource":{"primary":{"URL":"https:\/\/academic.oup.com\/comjnl\/article\/63\/9\/1355\/5614860"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,11,13]]},"references-count":27,"journal-issue":{"issue":"9","published-online":{"date-parts":[[2019,11,13]]},"published-print":{"date-parts":[[2020,8,20]]}},"URL":"https:\/\/doi.org\/10.1093\/comjnl\/bxz071","relation":{},"ISSN":["0010-4620","1460-2067"],"issn-type":[{"value":"0010-4620","type":"print"},{"value":"1460-2067","type":"electronic"}],"subject":[],"published-other":{"date-parts":[[2020,9]]},"published":{"date-parts":[[2019,11,13]]}}}