{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,6,17]],"date-time":"2025-06-17T08:12:16Z","timestamp":1750147936866,"version":"3.37.3"},"reference-count":23,"publisher":"Oxford University Press (OUP)","issue":"12","license":[{"start":{"date-parts":[[2022,10,7]],"date-time":"2022-10-07T00:00:00Z","timestamp":1665100800000},"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":["12271157","61772088"],"award-info":[{"award-number":["12271157","61772088"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2023,12,14]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>The generalized $k$-connectivity of a graph $G$, denoted by $\\kappa _k(G)$, is a generalization of the traditional connectivity and can serve for measuring the capability of a network $G$ to connect any $k$ vertices in $G$. It is well known that the generalized $k$-connectivity is an important indicator for measuring the fault tolerance and reliability of interconnection networks. The $n$-dimensional folded hypercube $FQ_n$, which is an important variation of hypercubes, can be obtained from the $n$-dimensional hypercube $Q_n$ by adding an edge between any pair of vertices with complementary addresses. In this paper, we show that $\\kappa _3(FQ_n)=n$ for $n\\ge 2$, that is, for any three vertices in $FQ_n$, there exist $n$ internally disjoint trees connecting them.<\/jats:p>","DOI":"10.1093\/comjnl\/bxac137","type":"journal-article","created":{"date-parts":[[2022,10,8]],"date-time":"2022-10-08T13:26:13Z","timestamp":1665235573000},"page":"2921-2927","source":"Crossref","is-referenced-by-count":1,"title":["The Generalized 3-Connectivity Of The Folded Hypercube <i>FQn<\/i>"],"prefix":"10.1093","volume":"66","author":[{"given":"Jing","family":"Wang","sequence":"first","affiliation":[{"name":"School of Computer Engineering and Applied Mathematics, Changsha University , Changsha 410022, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Fangmin","family":"Li","sequence":"additional","affiliation":[{"name":"School of Computer Engineering and Applied Mathematics, Changsha University , Changsha 410022, China"},{"name":"Hunan Province Key Laboratory of Industrial Internet Technology and Security, Changsha University , Changsha 410022, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"286","published-online":{"date-parts":[[2022,10,7]]},"reference":[{"key":"2023121811453290700_ref1","doi-asserted-by":"crossref","first-page":"167","DOI":"10.1007\/978-94-015-8937-6_5","volume-title":"Graph Symmetry: Algebraic Methods and Applications","author":"Heydemann","year":"1997"},{"issue":"1","key":"2023121811453290700_ref2","first-page":"179","article-title":"Algebraic properties and panconnectivity of folded hypercubes","volume":"95","author":"Ma","year":"2010","journal-title":"Ars Combin."},{"volume-title":"Introduction to parallel algorithms and architectures: Arrays, trees, hypercubes","year":"1992","author":"Leighton","key":"2023121811453290700_ref3"},{"key":"2023121811453290700_ref4","doi-asserted-by":"crossref","first-page":"57","DOI":"10.1016\/j.ins.2014.05.052","article-title":"Fault-tolerant cycles embedding in hypercubes with faulty edges","volume":"282","author":"Cheng","year":"2014","journal-title":"Inform. 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