{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,26]],"date-time":"2026-06-26T22:52:41Z","timestamp":1782514361837,"version":"3.54.5"},"reference-count":10,"publisher":"Oxford University Press (OUP)","issue":"5","license":[{"start":{"date-parts":[[2024,12,21]],"date-time":"2024-12-21T00:00:00Z","timestamp":1734739200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/academic.oup.com\/pages\/standard-publication-reuse-rights"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2025,5,15]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>Connectivity is an important parameter to measure fault-tolerance of networks. As a generalization, structure connectivity and substructure connectivity of networks were proposed. For connected graphs $G$ and $H$, the $H$-structure connectivity $\\kappa (G; H)$ (resp. $H$-substructure connectivity $\\kappa ^{s}(G; H)$) of $G$ is the minimum cardinality of a set of subgraphs $\\mathcal{F}$ of $G$ that each is isomorphic to $H$ (resp. a connected subgraph of $H$) such that $G-\\mathcal{F}$ is disconnected or the singleton. $n$-dimensional folded cross cube, $FCQ_{n}$, is a network obtained by adding edges to $n$-dimensional cross cubes. In this paper, we study star, path, and cycle structure connectivity and substructure connectivity of $FCQ_{n}$, where $n\\geq 8$. For star ($K_{1,m}$) structure, we get that $\\kappa (FCQ_{n}; K_{1, m})=\\kappa ^{s}(FCQ_{n}; K_{1, m})=\\lceil \\frac{n + 1}{2} \\rceil $ for $2 \\leq m \\leq \\frac{n}{2}$. For path ($P_{k}$) structure, we show that for $3\\leq k\\leq n+1$, if $k$ is odd, then $\\kappa (FCQ_{n}; P_{k})=\\kappa ^{s}(FCQ_{n}; P_{k})=\\lceil \\frac{2(n + 1)}{k+1}\\rceil $; if $k$ is even, then $\\kappa (FCQ_{n}; P_{k})=\\kappa ^{s}(FCQ_{n}; P_{k})=\\lceil \\frac{2(n + 1)} {k}\\rceil $. For cycle ($C_{k}$) structure, we prove that $\\kappa ^(FCQ_{n}; C_{k})=\\kappa ^{s}(FCQ_{n}; P_{k})$. Further, we calculate $\\kappa ^(FCQ_{n}; C_{2k-1})=\\lceil \\frac{n+1}{k-1} \\rceil $ for $4 \\leq k \\leq n+2$ and $C_{2k}$-structure connectivity of $FCQ_{n}$ is $\\lfloor \\frac{n+1}{k} \\rfloor +1$ for $6 \\leq k\\leq n + 1$ and even $k$.<\/jats:p>","DOI":"10.1093\/comjnl\/bxae127","type":"journal-article","created":{"date-parts":[[2024,12,22]],"date-time":"2024-12-22T09:39:22Z","timestamp":1734860362000},"page":"502-509","source":"Crossref","is-referenced-by-count":3,"title":["Structure connectivity of folded cross cubes"],"prefix":"10.1093","volume":"68","author":[{"given":"Lina","family":"Ba","sequence":"first","affiliation":[{"name":"School of Finance and Mathematics, Huainan Normal University , Huainan, Anhui 232038 ,","place":["China"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Heping","family":"Zhang","sequence":"additional","affiliation":[{"name":"School of Mathematics and Statistics, Lanzhou University , Lanzhou, Gansu 730000 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