{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,31]],"date-time":"2026-03-31T06:42:51Z","timestamp":1774939371235,"version":"3.50.1"},"reference-count":35,"publisher":"Oxford University Press (OUP)","issue":"12","license":[{"start":{"date-parts":[[2024,9,14]],"date-time":"2024-09-14T00:00:00Z","timestamp":1726272000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/academic.oup.com\/pages\/standard-publication-reuse-rights"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["12001464"],"award-info":[{"award-number":["12001464"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100004735","name":"Natural Science Foundation of Hunan Province","doi-asserted-by":"publisher","award":["2022JJ40418"],"award-info":[{"award-number":["2022JJ40418"]}],"id":[{"id":"10.13039\/501100004735","id-type":"DOI","asserted-by":"publisher"}]},{"name":"General Research Project of Hunan Provincial Department of Education","award":["20C1766"],"award-info":[{"award-number":["20C1766"]}]},{"name":"Doctor\u2019s Funds of Xiangtan University","award":["09KZ|KZ08069"],"award-info":[{"award-number":["09KZ|KZ08069"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2024,12,20]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>The connectivity is an important measurement for the fault-tolerance of networks. To provide more accurate measures for the fault-tolerance of networks than the connectivity, some generalizations of connectivity have been introduced. Substructure connectivity and structure connectivity are two extended concepts of classical connectivity. As a variant of the popular network hypercube, the M\u00f6bius cubes is also a famous interconnection network in parallel and distributed systems. In this article, we calculate $H$-substructure connectivity and $H$-structure connectivity of M\u00f6bius cubes when $H$ is isomorphic to $P_{m},C_{m}$ and $K_{1,m}$.<\/jats:p>","DOI":"10.1093\/comjnl\/bxae083","type":"journal-article","created":{"date-parts":[[2024,9,15]],"date-time":"2024-09-15T07:43:50Z","timestamp":1726386230000},"page":"3207-3220","source":"Crossref","is-referenced-by-count":2,"title":["Structure connectivity and substructure connectivity of M\u00f6bius cubes"],"prefix":"10.1093","volume":"67","author":[{"given":"Xiaojun","family":"Zhao","sequence":"first","affiliation":[{"name":"School of Mathematics , Hunan University Changsha, Hunan 410082, P. R.","place":["China"]}]},{"given":"Shudan","family":"Xue","sequence":"additional","affiliation":[{"name":"Center for Combinatorics , Nankai University Tianjin 300071, P. 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