{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,5,23]],"date-time":"2025-05-23T17:06:44Z","timestamp":1748020004081,"version":"3.37.3"},"reference-count":13,"publisher":"Oxford University Press (OUP)","issue":"12","license":[{"start":{"date-parts":[[2023,3,10]],"date-time":"2023-03-10T00:00:00Z","timestamp":1678406400000},"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 Science Foundation of China","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":[[2023,12,14]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>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 $G$ such that each is isomorphic to $H$ (resp. to a connected subgraph of $H$) so that $G-\\mathcal{F}$ is disconnected or singleton. In this paper, we consider $P_t$-structure connectivity and $P_t$-substructure connectivity of augmented $k$-ary $n$-cubes $AQ_{n,k}$ for $n\\geq 2$, $k\\geq 3$ and $1\\leq t\\leq 4n-2$. We obtain that $\\kappa (AQ_{n,k}; P_t)=\\kappa ^s(AQ_{n,k}; P_t)=\\frac{4n-2}{t}+1$ for $t\\mid 4n-2$, $t\\nmid 2n-1$, $t&amp;gt;6$, $n\\geq 3$ and $k\\geq 4$; $\\kappa (AQ_{n,k}; P_t)=\\kappa ^s(AQ_{n,k}; P_t)=\\lceil \\frac{4n-2}{t}\\rceil $, in other cases.<\/jats:p>","DOI":"10.1093\/comjnl\/bxac197","type":"journal-article","created":{"date-parts":[[2023,3,11]],"date-time":"2023-03-11T08:12:34Z","timestamp":1678522354000},"page":"3119-3128","source":"Crossref","is-referenced-by-count":1,"title":["The Path-Structure Connectivity of Augmented <i>k<\/i>-ary <i>n<\/i>-cubes"],"prefix":"10.1093","volume":"66","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":"Yaxian","family":"Zhang","sequence":"additional","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. China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"286","published-online":{"date-parts":[[2023,3,10]]},"reference":[{"key":"2023121811455409600_ref1","doi-asserted-by":"crossref","first-page":"347","DOI":"10.1002\/net.3230130303","article-title":"Conditional connectivity","volume":"13","author":"Harary","year":"1983","journal-title":"Network"},{"key":"2023121811455409600_ref2","doi-asserted-by":"crossref","first-page":"97","DOI":"10.1016\/j.tcs.2016.04.014","article-title":"Structure connectivity and substructure connectivity of hypercubes","volume":"634","author":"Lin","year":"2016","journal-title":"Theoret. Comput. 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Sci."},{"key":"2023121811455409600_ref6","doi-asserted-by":"crossref","first-page":"169","DOI":"10.1016\/j.tcs.2019.09.007","article-title":"Structure connectivity and substructure connectivity of twisted hypercubes","volume":"796","author":"Li","year":"2019","journal-title":"Theoret. Comput. Sci."},{"key":"2023121811455409600_ref7","doi-asserted-by":"crossref","first-page":"115","DOI":"10.1016\/j.ins.2017.11.047","article-title":"Structure connectivity and substructure connectivity of $k$-ary $n$-cube networks","volume":"433-434","author":"Lv","year":"2018","journal-title":"Inform. Sci."},{"key":"2023121811455409600_ref8","doi-asserted-by":"crossref","first-page":"134496","DOI":"10.1109\/ACCESS.2019.2941711","article-title":"Structure connectivity and substructure connectivity of $k$-ary $n$-cube networks","volume":"7","author":"Zhang","year":"2019","journal-title":"IEEE Access"},{"key":"2023121811455409600_ref9","first-page":"124632","article-title":"Structure connectivity and substructure connectivity of bubble-sort star graph networks","volume":"363","author":"Zhang","year":"2019","journal-title":"Appl. Math Comput."},{"key":"2023121811455409600_ref10","doi-asserted-by":"crossref","first-page":"240","DOI":"10.1109\/I-SPAN.2018.00046","article-title":"Structure connectivity and substructure connectivity of $\\left (n,k\\right )$-star graph networks","volume-title":"2018 15th International Symposium on Pervasive Systems, Algorithms and Networks (I-SPAN) IEEE","author":"Li","year":"2018"},{"key":"2023121811455409600_ref11","doi-asserted-by":"crossref","first-page":"239","DOI":"10.1016\/j.ins.2010.09.005","article-title":"Augmented $k$-ary $n$-cube","volume":"181","author":"Xiang","year":"2011","journal-title":"Inform. 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J."}],"container-title":["The Computer Journal"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/academic.oup.com\/comjnl\/article-pdf\/66\/12\/3119\/54446731\/bxac197.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"https:\/\/academic.oup.com\/comjnl\/article-pdf\/66\/12\/3119\/54446731\/bxac197.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,12,18]],"date-time":"2023-12-18T11:47:00Z","timestamp":1702900020000},"score":1,"resource":{"primary":{"URL":"https:\/\/academic.oup.com\/comjnl\/article\/66\/12\/3119\/7075448"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,3,10]]},"references-count":13,"journal-issue":{"issue":"12","published-online":{"date-parts":[[2023,3,10]]},"published-print":{"date-parts":[[2023,12,14]]}},"URL":"https:\/\/doi.org\/10.1093\/comjnl\/bxac197","relation":{},"ISSN":["0010-4620","1460-2067"],"issn-type":[{"type":"print","value":"0010-4620"},{"type":"electronic","value":"1460-2067"}],"subject":[],"published-other":{"date-parts":[[2023,12]]},"published":{"date-parts":[[2023,3,10]]}}}