{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,14]],"date-time":"2026-02-14T00:50:10Z","timestamp":1771030210747,"version":"3.50.1"},"reference-count":18,"publisher":"Oxford University Press (OUP)","issue":"12","license":[{"start":{"date-parts":[[2021,9,15]],"date-time":"2021-09-15T00:00:00Z","timestamp":1631664000000},"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":"NSFC","doi-asserted-by":"publisher","award":["11871256"],"award-info":[{"award-number":["11871256"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"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>As a generalization of vertex connectivity, for connected graphs $G$ and $T$, the $T$-structure connectivity $\\kappa (G; T)$ (resp. $T$-substructure connectivity $\\kappa ^{s}(G; T)$) of $G$ is the minimum cardinality of a set of subgraphs $F$ of $G$ that each is isomorphic to $T$ (resp. to a connected subgraph of $T$) so that $G-F$ is disconnected. For $n$-dimensional hypercube $Q_{n}$, Lin et al. showed $\\kappa (Q_{n};K_{1,1})=\\kappa ^{s}(Q_{n};K_{1,1})=n-1$ and $\\kappa (Q_{n};K_{1,r})=\\kappa ^{s}(Q_{n};K_{1,r})=\\lceil \\frac{n}{2}\\rceil $ for $2\\leq r\\leq 3$ and $n\\geq 3$ (Lin, C.-K., Zhang, L.-L., Fan, J.-X. and Wang, D.-J. (2016) Structure connectivity and substructure connectivity of hypercubes. Theor. Comput. Sci., 634, 97\u2013107). Sabir et al. obtained that $\\kappa (Q_{n};K_{1,4})=\\kappa ^{s}(Q_{n};K_{1,4})= \\lceil \\frac{n}{2}\\rceil $ for $n\\geq 6$ and for $n$-dimensional folded hypercube $FQ_{n}$, $\\kappa (FQ_{n};K_{1,1})=\\kappa ^{s}(FQ_{n};K_{1,1})=n$, $\\kappa (FQ_{n};K_{1,r})=\\kappa ^{s}(FQ_{n};K_{1,r})= \\lceil \\frac{n+1}{2}\\rceil $ with $2\\leq r\\leq 3$ and $n\\geq 7$ (Sabir, E. and Meng, J.(2018) Structure fault tolerance of hypercubes and folded hypercubes. Theor. Comput. Sci., 711, 44\u201355). They proposed an open problem of determining $K_{1,r}$-structure connectivity of $Q_n$ and $FQ_n$ for general $r$. In this paper, we obtain that for each integer $r\\geq 2$, $\\kappa (Q_{n};K_{1,r})$ \u00a0$=\\kappa ^{s}(Q_{n};K_{1,r})$ \u00a0$=\\lceil \\frac{n}{2}\\rceil $ and $\\kappa (FQ_{n};K_{1,r})=\\kappa ^{s}(FQ_{n};K_{1,r})= \\lceil \\frac{n+1}{2}\\rceil $ for all integers $n$ larger than $r$ in quare scale. For $4\\leq r\\leq 6$, we separately confirm the above result holds for $Q_n$ in the remaining cases.<\/jats:p>","DOI":"10.1093\/comjnl\/bxab133","type":"journal-article","created":{"date-parts":[[2021,9,8]],"date-time":"2021-09-08T11:19:10Z","timestamp":1631099950000},"page":"3156-3166","source":"Crossref","is-referenced-by-count":10,"title":["The Star-Structure Connectivity and Star-Substructure Connectivity of Hypercubes and Folded Hypercubes"],"prefix":"10.1093","volume":"65","author":[{"given":"Lina","family":"Ba","sequence":"first","affiliation":[{"name":"School of Mathematics and Statistics , Lanzhou University, Lanzhou, Gansu 730000, P.R. China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Heping","family":"Zhang","sequence":"additional","affiliation":[{"name":"School of Mathematics and Statistics , Lanzhou University, Lanzhou, Gansu 730000, P.R. 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