{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,5]],"date-time":"2025-10-05T12:33:12Z","timestamp":1759667592918,"version":"3.37.3"},"reference-count":30,"publisher":"Oxford University Press (OUP)","issue":"10","license":[{"start":{"date-parts":[[2024,7,9]],"date-time":"2024-07-09T00:00:00Z","timestamp":1720483200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/academic.oup.com\/pages\/standard-publication-reuse-rights"}],"funder":[{"DOI":"10.13039\/501100001809","name":"Natural Science Foundation of China","doi-asserted-by":"publisher","award":["62302235","62202250"],"award-info":[{"award-number":["62302235","62202250"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100004608","name":"Natural Science Foundation of Jiangsu Province","doi-asserted-by":"publisher","award":["BK20230352","BK20200753"],"award-info":[{"award-number":["BK20230352","BK20200753"]}],"id":[{"id":"10.13039\/501100004608","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Natural Science Research Start-up Foundation of Recruiting Talents of Nanjing University of Posts and Telecommunications","award":["NY222064","NY222065"],"award-info":[{"award-number":["NY222064","NY222065"]}]},{"name":"National Science Foundation of Shandong Province","award":["ZR2021QF079"],"award-info":[{"award-number":["ZR2021QF079"]}]},{"name":"Talent Cultivation Promotion Program of Computer Science and Technology in Qilu University of Technology","award":["2023PY059"],"award-info":[{"award-number":["2023PY059"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2024,10,12]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>Connectivity is a meaningful metric parameter and indicator for estimating network reliability and evaluating network fault tolerance. However, the traditional connectivity and current conditional connectivity do not take into account the association between a certain node and its neighboring nodes. In fact, adjacent nodes are easily influenced by each other so that the failing probability of adjacent nodes around a faulty node is high. Therefore, cluster and super cluster connectivities are proposed to more intuitively measure the fault tolerance of the network. In this paper, we mainly explore the cluster connectivity and super cluster connectivity of the hierarchical cubic network $HCN_{n}$. In detail, we show that $\\kappa (HCN_{n}\\mid K_{1, 0}(K_{1, 0}^{*}))=n+1$, $\\kappa (HCN_{n}\\mid K_{1, 1}(K_{1, 1}^{*}))=\\kappa ^{\\prime}(HCN_{n}\\mid K_{1, 1}(K_{1, 1}^{*}))=n+1$, $\\kappa (HCN_{n}\\mid K_{1, m}(K_{1, m}^{*}))=\\lceil n\/2\\rceil +1$ ($2\\leq m\\leq 4$), $\\kappa ^{\\prime}(HCN_{n}\\mid K_{1, 0}(K_{1, 0}^{*}))=2n$, and $\\kappa ^{\\prime}(HCN_{n}\\mid K_{1, m}(K_{1, m}^{*}))=n+1$ ($2\\leq m\\leq 3$) if $n$ is odd and $\\kappa ^{\\prime}(HCN_{n}\\mid K_{1, m}(K_{1, m}^{*}))=n$ ($2\\leq m\\leq 3$) if $n$ is even, where $n\\geq 4$.<\/jats:p>","DOI":"10.1093\/comjnl\/bxae054","type":"journal-article","created":{"date-parts":[[2024,10,1]],"date-time":"2024-10-01T09:55:45Z","timestamp":1727776545000},"page":"2890-2897","source":"Crossref","is-referenced-by-count":3,"title":["Fault tolerance of hierarchical cubic networks based on cluster fault pattern"],"prefix":"10.1093","volume":"67","author":[{"given":"Mengjie","family":"Lv","sequence":"first","affiliation":[{"name":"College of Computer, Nanjing University of Posts and Telecommunications , Nanjing 210003 ,","place":["China"]}]},{"given":"Weibei","family":"Fan","sequence":"additional","affiliation":[{"name":"College of Computer, Nanjing University of Posts and Telecommunications , Nanjing 210003 ,","place":["China"]}]},{"given":"Hui","family":"Dong","sequence":"additional","affiliation":[{"name":"College of Computer, Nanjing University of Posts and Telecommunications , Nanjing 210003 ,","place":["China"]}]},{"given":"Guijuan","family":"Wang","sequence":"additional","affiliation":[{"name":"Key Laboratory of Computing Power Network and Information Security , Ministry of Education, Shandong Computer Science Center, Qilu University of Technology (Shandong Academy of Sciences), Jinan 250353 ,","place":["China"]},{"name":"Shandong Provincial Key Laboratory of Computer Networks , Shandong Fundamental Research Center for Computer Science, Jinan 250353 ,","place":["China"]}]}],"member":"286","published-online":{"date-parts":[[2024,7,9]]},"reference":[{"key":"2024101809310896300_ref1","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-84628-970-5","volume-title":"Graph theory","author":"Bondy","year":"2008"},{"key":"2024101809310896300_ref2","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":"2024101809310896300_ref3","doi-asserted-by":"crossref","first-page":"49","DOI":"10.1016\/0012-365X(94)00369-T","article-title":"On the extraconnectivity of graphs","volume":"155","author":"F\u00e0brega","year":"1996","journal-title":"Discret Math"},{"key":"2024101809310896300_ref4","first-page":"1","article-title":"Generalized connectivity in 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