{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,3]],"date-time":"2026-03-03T17:21:25Z","timestamp":1772558485171,"version":"3.50.1"},"reference-count":32,"publisher":"Oxford University Press (OUP)","issue":"12","license":[{"start":{"date-parts":[[2021,10,5]],"date-time":"2021-10-05T00:00:00Z","timestamp":1633392000000},"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\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["62172291"],"award-info":[{"award-number":["62172291"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["U1905211"],"award-info":[{"award-number":["U1905211"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Natural Science Foundation"},{"name":"Jiangsu Higher Education Institutions of China","award":["18KJA520009"],"award-info":[{"award-number":["18KJA520009"]}]},{"name":"Collaborative Innovation Center of Novel Software Technology and Industrialization"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2022,12,30]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>Connectivity is a significant metric to assess the fault tolerance of a network. For a faulty vertex set $H$, the $h$-extra connectivity is defined under the assumption that every component of the network removing $H$ has at least $h+1$ fault-free vertices. Compared to the traditional connectivity, which is defined under the assumption that the network removing $H$ is disconnected or trivial, the $h$-extra connectivity can better reflect the true fault tolerance of the network. The $BCube$ is an important server-centric data center network; it has good fault tolerance and scalability. In this paper, our research focuses on the logical structure of $BCube$, named $BC_{n,k}$, which is actually a specific type of generalized hypercubes. We prove that the 3-extra connectivity of $BC_{n,k}$ is $4(k+1)(n-1)-4n$ for $k\\geq 4$ and $n\\geq 4$.<\/jats:p>","DOI":"10.1093\/comjnl\/bxab137","type":"journal-article","created":{"date-parts":[[2021,9,9]],"date-time":"2021-09-09T12:09:16Z","timestamp":1631189356000},"page":"3199-3208","source":"Crossref","is-referenced-by-count":22,"title":["The 3-Extra Connectivity of the Data Center Network BCube"],"prefix":"10.1093","volume":"65","author":[{"given":"Yi","family":"Yi","sequence":"first","affiliation":[{"name":"School of Computer Science and Technology , Soochow University, Suzhou 215006, China"}]},{"given":"Jianxi","family":"Fan","sequence":"additional","affiliation":[{"name":"School of Computer Science and Technology , Soochow University, Suzhou 215006, China"}]},{"given":"Baolei","family":"Cheng","sequence":"additional","affiliation":[{"name":"School of Computer Science and Technology , Soochow University, Suzhou 215006, China"}]},{"given":"Yan","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Computer Science and Technology , Soochow University, Suzhou 215006, China"}]},{"given":"Jia","family":"Yu","sequence":"additional","affiliation":[{"name":"College of Computer Science and Technology , Qingdao University, Qingdao 266071, China"}]}],"member":"286","published-online":{"date-parts":[[2021,10,5]]},"reference":[{"key":"2023010312520609800_ref1","first-page":"29","volume-title":"Proc. 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SIGCOMM\u201909, Barcelona, Spain, August 17\u201321","author":"Guo","year":"2009"},{"key":"2023010312520609800_ref6","doi-asserted-by":"crossref","first-page":"1105","DOI":"10.1109\/TPDS.2018.2874659","article-title":"HSDC: A highly scalable data center network architecture for greater incremental scalability","volume":"30","author":"Zhang","year":"2019","journal-title":"IEEE Trans. Parallel Distributed Syst."},{"key":"2023010312520609800_ref7","doi-asserted-by":"crossref","first-page":"2132","DOI":"10.1016\/j.comnet.2012.02.016","article-title":"DPillar: Dual-port server interconnection network for large scale data centers","volume":"56","author":"Liao","year":"2012","journal-title":"Comput. Netw."},{"key":"2023010312520609800_ref8","doi-asserted-by":"crossref","first-page":"77","DOI":"10.1109\/TNET.2016.2547438","article-title":"BCCC: An expandable network for data centers","volume":"24","author":"Li","year":"2016","journal-title":"IEEE\/ACM Trans. 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Sci."},{"key":"2023010312520609800_ref16","volume-title":"Research on conditional connectivity and fault-tolerant routing of generalized hypercubes","author":"Guo","year":"2018"},{"key":"2023010312520609800_ref17","doi-asserted-by":"crossref","first-page":"1064","DOI":"10.1007\/s11390-020-9508-3","article-title":"The fault-tolerant hamiltonicity and hamiltonian connectivity of BCube with various faulty elements","volume":"35","author":"Wang","year":"2020","journal-title":"J. Comput. Sci. Tec."},{"key":"2023010312520609800_ref18","doi-asserted-by":"crossref","first-page":"55","DOI":"10.1016\/j.tcs.2013.08.004","article-title":"Two spanning disjoint paths with required length in generalized hypercubes","volume":"506","author":"Duh","year":"2013","journal-title":"Theor. Comput. 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