{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,13]],"date-time":"2026-02-13T13:03:19Z","timestamp":1770987799686,"version":"3.50.1"},"reference-count":24,"publisher":"Oxford University Press (OUP)","issue":"2","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":[{"name":"Youth Project of Hunan Provincial Natural Science Foundation of China","award":["2021JJ40522"],"award-info":[{"award-number":["2021JJ40522"]}]},{"name":"Project of Education Department of Hunan Province","award":["22B0180"],"award-info":[{"award-number":["22B0180"]}]},{"name":"Project of Scientific Research Fund of Hunan Provincial Science and Technology Department","award":["2018WK4006"],"award-info":[{"award-number":["2018WK4006"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2024,2,17]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>Edge connectivity is an important parameter for the reliability of the inter-connection network. A graph $G$ is strong Menger edge-connected ($SM$-$\\lambda $ for short) if there exist min$\\{\\deg _{G}(u),\\deg _{G}(v)\\}$ edge-disjoint paths between any pair of vertices $u$ and $v$ of $G$. The conditional edge-fault-tolerance strong Menger edge connectivity of $G$, denoted by $sm_{\\lambda }^{r}(G)$, is the maximum integer $m$ such that $G-F$ remains $SM$-$\\lambda $ for any edge set $F$ with $|F|\\leq m$ and $\\delta (G-F)\\geq r$, where $\\delta (G-F)\\geq r$ is the minimum degree of $G-F$. Most of the previous papers discussed $sm_{\\lambda }^{r}(G)$ in the case of $r\\leq 2$. In this paper, we show that $sm_{\\lambda }^{r}(FQ_{n})=2^{r}(n-r+1)-(n+1)$ for $1\\leq r\\leq n-2$, where $n\\geq 4$.<\/jats:p>","DOI":"10.1093\/comjnl\/bxad018","type":"journal-article","created":{"date-parts":[[2023,3,13]],"date-time":"2023-03-13T15:47:57Z","timestamp":1678722477000},"page":"777-781","source":"Crossref","is-referenced-by-count":3,"title":["On Conditional Edge-Fault-Tolerant Strong Menger Edge Connectivity Of Folded Hypercubes"],"prefix":"10.1093","volume":"67","author":[{"given":"Shijie","family":"Zhao","sequence":"first","affiliation":[{"name":"Key Laboratory of Intelligent Computing Information Processing of Education School of Mathematics and Computational Science, Xiangtan University , Xiangtan, Hunan 411105, PR China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Pingshan","family":"Li","sequence":"additional","affiliation":[{"name":"Key Laboratory of Intelligent Computing Information Processing of Education School of Mathematics and Computational Science, Xiangtan University , Xiangtan, Hunan 411105, PR China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"286","published-online":{"date-parts":[[2023,3,10]]},"reference":[{"key":"2024021913320420700_ref1","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-349-03521-2","volume-title":"Graph theory with applications","author":"Bondy","year":"1976"},{"key":"2024021913320420700_ref2","article-title":"The edge-connectivity, average-connectivity and degree conditions","author":"Fricke","year":"2000","journal-title":"Unpublished manuscript"},{"key":"2024021913320420700_ref3","first-page":"295","article-title":"Maximally local-edge-connected graphs and digraphs","volume":"72","author":"Hellwig","year":"2004","journal-title":"Ars Combin."},{"key":"2024021913320420700_ref4","doi-asserted-by":"crossref","first-page":"112681","DOI":"10.1016\/j.disc.2021.112681","article-title":"Edge fault-tolerance of strongly Menger edge connected graphs","volume":"345","author":"Li","year":"2022","journal-title":"Discrete Math."},{"key":"2024021913320420700_ref5","doi-asserted-by":"crossref","first-page":"22","DOI":"10.1016\/j.comcom.2015.05.007","article-title":"A survey on fault tolerance in small and large scale wireless sensor networks","volume":"69","author":"Chouikhi","year":"2015","journal-title":"Comput. Commun."},{"key":"2024021913320420700_ref6","doi-asserted-by":"crossref","first-page":"28","DOI":"10.1145\/2522968.2522976","article-title":"Methods for fault tolerance in networks-on-chip","volume":"46","author":"Radetzki","year":"2013","journal-title":"ACM Comput. Surv."},{"key":"2024021913320420700_ref7","doi-asserted-by":"crossref","first-page":"1646","DOI":"10.1162\/0899766053723096","article-title":"Investigating the fault tolerance of neural networks","volume":"17","author":"Tchernev","year":"2005","journal-title":"Neural Comput."},{"key":"2024021913320420700_ref8","doi-asserted-by":"crossref","first-page":"1124","DOI":"10.1137\/0216071","article-title":"Almost sure fault tolerance in random graphs","volume":"16","author":"Scheinerman","year":"1987","journal-title":"SIAM J. Comput."},{"key":"2024021913320420700_ref9","doi-asserted-by":"crossref","first-page":"998","DOI":"10.1016\/j.ipl.2010.08.010","article-title":"A kind of conditional fault tolerance of alternating group graphs","volume":"110","author":"Zhang","year":"2010","journal-title":"Inform. Process. Lett."},{"key":"2024021913320420700_ref10","doi-asserted-by":"crossref","first-page":"208","DOI":"10.1016\/j.jcss.2017.04.002","article-title":"On g-extra connectivity of hypercube-like networks","volume":"88","author":"Zhou","year":"2017","journal-title":"J. Comput. Syst. Sci."},{"key":"2024021913320420700_ref11","doi-asserted-by":"crossref","first-page":"50","DOI":"10.1016\/j.tcs.2018.04.001","article-title":"Strongly Menger-edge-connectedness and strongly Menger-vertex-connectedness of regular networks","volume":"731","author":"He","year":"2018","journal-title":"Theoret. Comput. Sci."},{"key":"2024021913320420700_ref12","first-page":"96","article-title":"Edge disjoint paths in hypercubes and folded hypercubes with conditional faults","volume":"294","author":"Qiao","year":"2017","journal-title":"Appl. Math. Comput."},{"key":"2024021913320420700_ref13","article-title":"Edge-fault-tolerance about the $SM$-$\\lambda $ property of hypercube-like networks","author":"Liu","year":"2020","journal-title":"manuscript"},{"key":"2024021913320420700_ref14","doi-asserted-by":"crossref","first-page":"56","DOI":"10.1016\/j.tcs.2017.10.017","article-title":"Fault-tolerant strong Menger (edge) connectivity and 3-extra edge-connectivity of balanced hypercubes","volume":"707","author":"Li","year":"2018","journal-title":"Theoret. Comput. Sci."},{"key":"2024021913320420700_ref15","doi-asserted-by":"crossref","first-page":"109","DOI":"10.1016\/j.dam.2021.03.006","article-title":"Edge-fault-tolerant strong Menger edge connectivity of bubble-sort star graphs","volume":"297","author":"Guo","year":"2021","journal-title":"Discret. Appl. Math."},{"issue":"12","key":"2024021913320420700_ref16","doi-asserted-by":"crossref","first-page":"13210","DOI":"10.3934\/math.2021763","article-title":"Edge-fault-tolerant strong Menger edge connectivity of bubble-sort graphs","volume":"6","author":"Wang","year":"2021","journal-title":"AIMS Math."},{"issue":"5","key":"2024021913320420700_ref17","doi-asserted-by":"crossref","first-page":"812","DOI":"10.1093\/comjnl\/bxaa037","article-title":"Strong Menger connectedness of augmented k-ary n-cubes","volume":"64","author":"Gu","year":"2021","journal-title":"Comput. J."},{"key":"2024021913320420700_ref18","doi-asserted-by":"crossref","first-page":"94","DOI":"10.1016\/j.tcs.2019.09.047","article-title":"Strongly Menger connectedness of data center network and (n, k)-star graph","volume":"799","author":"Gu","year":"2019","journal-title":"Theoret. Comput. Sci."},{"key":"2024021913320420700_ref19","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.tcs.2018.03.011","article-title":"Conditional (edge-) fault-tolerant strong Menger (edge) connectivity of folded hypercubes","volume":"728","author":"Cheng","year":"2018","journal-title":"Theoret. Comput. Sci."},{"issue":"04","key":"2024021913320420700_ref20","doi-asserted-by":"crossref","first-page":"323","DOI":"10.1109\/TC.1984.1676437","article-title":"Generalized hypercube and hypercubs structures for a computer network","volume":"33","author":"Bhuyan","year":"1984","journal-title":"IEEE Trans. Comput."},{"key":"2024021913320420700_ref21","doi-asserted-by":"crossref","first-page":"31","DOI":"10.1109\/71.80187","article-title":"Properties and performance of folded hypercubes","volume":"2","author":"El-Amawy","year":"1991","journal-title":"IEEE Trans. Parallel Distrib. Syst."},{"key":"2024021913320420700_ref22","doi-asserted-by":"crossref","first-page":"2753","DOI":"10.1016\/j.dam.2013.04.009","article-title":"Bounding the size of the subgraph induced by m vertices and extra edge-connectivity of hypercubes","volume":"161","author":"Li","year":"2013","journal-title":"Discrete Appl. Math."},{"key":"2024021913320420700_ref23","article-title":"Component edge connectivity of the folded hypercube","author":"Zhao","year":"2018","journal-title":"arXiv preprint arXiv:1803.01312"},{"key":"2024021913320420700_ref24","doi-asserted-by":"crossref","first-page":"96","DOI":"10.4064\/fm-10-1-96-115","article-title":"Zur allgemeinen Kurventheorie","volume":"10","author":"Menger","year":"1927","journal-title":"Fund. Math."}],"container-title":["The Computer Journal"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/academic.oup.com\/comjnl\/article-pdf\/67\/2\/777\/56701495\/bxad018.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"https:\/\/academic.oup.com\/comjnl\/article-pdf\/67\/2\/777\/56701495\/bxad018.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,2,19]],"date-time":"2024-02-19T13:36:58Z","timestamp":1708349818000},"score":1,"resource":{"primary":{"URL":"https:\/\/academic.oup.com\/comjnl\/article\/67\/2\/777\/7075451"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,3,10]]},"references-count":24,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2023,3,10]]},"published-print":{"date-parts":[[2024,2,17]]}},"URL":"https:\/\/doi.org\/10.1093\/comjnl\/bxad018","relation":{},"ISSN":["0010-4620","1460-2067"],"issn-type":[{"value":"0010-4620","type":"print"},{"value":"1460-2067","type":"electronic"}],"subject":[],"published-other":{"date-parts":[[2024,2]]},"published":{"date-parts":[[2023,3,10]]}}}