{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,13]],"date-time":"2026-10-13T20:25:40Z","timestamp":1791923140867,"version":"4.3.4"},"reference-count":24,"publisher":"Oxford University Press (OUP)","issue":"9","license":[{"start":{"date-parts":[[2019,9,4]],"date-time":"2019-09-04T00:00:00Z","timestamp":1567555200000},"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\/501100002858","name":"China Postdoctoral Science Foundation","doi-asserted-by":"publisher","award":["2018M631322"],"award-info":[{"award-number":["2018M631322"]}],"id":[{"id":"10.13039\/501100002858","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100004663","name":"Ministry of Science and Technology, Taiwan","doi-asserted-by":"publisher","award":["MOST-107-2221-E-141-001-MY3"],"award-info":[{"award-number":["MOST-107-2221-E-141-001-MY3"]}],"id":[{"id":"10.13039\/501100004663","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11731002"],"award-info":[{"award-number":["11731002"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"111 Project of China","award":["B16002"],"award-info":[{"award-number":["B16002"]}]}],"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>For an integer $\\ell \\geqslant 2$, the $\\ell $-component connectivity (resp. $\\ell $-component edge connectivity) of a graph $G$, denoted by $\\kappa _{\\ell }(G)$ (resp. $\\lambda _{\\ell }(G)$), is the minimum number of vertices (resp. edges) whose removal from $G$ results in a disconnected graph with at least $\\ell $ components. The two parameters naturally generalize the classical connectivity and edge connectivity of graphs defined in term of the minimum vertex-cut and the minimum edge-cut, respectively. The two kinds of connectivities can help us to measure the robustness of the graph corresponding to a network. In this paper, by exploring algebraic and combinatorial properties of $n$-dimensional balanced hypercubes $BH_n$, we obtain the $\\ell $-component (edge) connectivity $\\kappa _{\\ell }(BH_n)$ ($\\lambda _{\\ell }(BH_n)$). For $\\ell $-component connectivity, we prove that $\\kappa _2(BH_n)=\\kappa _3(BH_n)=2n$ for $n\\geq 2$, $\\kappa _4(BH_n)=\\kappa _5(BH_n)=4n-2$ for $n\\geq 4$, $\\kappa _6(BH_n)=\\kappa _7(BH_n)=6n-6$ for $n\\geq 5$. For $\\ell $-component edge connectivity, we prove that $\\lambda _3(BH_n)=4n-1$, $\\lambda _4(BH_n)=6n-2$ for $n\\geq 2$ and $\\lambda _5(BH_n)=8n-4$ for $n\\geq 3$. Moreover, we also prove $\\lambda _\\ell (BH_n)\\leq 2n(\\ell -1)-2\\ell +6$ for $4\\leq \\ell \\leq 2n+3$ and the upper bound of $\\lambda _\\ell (BH_n)$ we obtained is tight for $\\ell =4,5$.<\/jats:p>","DOI":"10.1093\/comjnl\/bxz058","type":"journal-article","created":{"date-parts":[[2019,5,14]],"date-time":"2019-05-14T07:17:44Z","timestamp":1557818264000},"page":"1311-1320","source":"Crossref","is-referenced-by-count":35,"title":["On Computing Component (Edge) Connectivities of Balanced Hypercubes"],"prefix":"10.1093","volume":"63","author":[{"given":"Mei-Mei","family":"Gu","sequence":"first","affiliation":[{"name":"Department of Mathematics, Beijing Jiaotong University, Beijing 100044, P.R. China"},{"name":"Faculty of Mathematics and Physics, Charles University, Prague 11800, Czech Republic"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jou-Ming","family":"Chang","sequence":"additional","affiliation":[{"name":"Institute of Information and Decision Sciences, National Taipei University of Business, Taipei 10051, Taiwan"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Rong-Xia","family":"Hao","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Beijing Jiaotong University, Beijing 100044, P.R. China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"286","published-online":{"date-parts":[[2019,9,4]]},"reference":[{"key":"2020091506340997400_ref1","first-page":"1","article-title":"Generalized connectivity in graphs","volume":"2","author":"Chartrand","year":"1984","journal-title":"Bull. Bombay Math. 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