{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,13]],"date-time":"2026-01-13T15:25:06Z","timestamp":1768317906081,"version":"3.49.0"},"reference-count":29,"publisher":"Oxford University Press (OUP)","issue":"9","license":[{"start":{"date-parts":[[2022,6,12]],"date-time":"2022-06-12T00:00:00Z","timestamp":1654992000000},"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\/100009110","name":"Natural Science Foundation of Xinjiang Province","doi-asserted-by":"publisher","award":["2020D04046"],"award-info":[{"award-number":["2020D04046"]}],"id":[{"id":"10.13039\/100009110","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["12101528"],"award-info":[{"award-number":["12101528"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Science and Technology Project of Xinjiang Uygur Autonomous Region","award":["2020D01C069"],"award-info":[{"award-number":["2020D01C069"]}]},{"name":"Doctoral Startup Foundation of Xinjiang University","award":["62031224736"],"award-info":[{"award-number":["62031224736"]}]},{"name":"Tianchi Ph.D Program","award":["tcbs201905"],"award-info":[{"award-number":["tcbs201905"]}]},{"name":"Xinjiang Key Laboratory of Applied Mathematics","award":["XJDX1401"],"award-info":[{"award-number":["XJDX1401"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2023,9,18]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>The conditional edge-connectivity is an important parameter to evaluate the reliability and fault tolerance of multi-processor systems. The $n$-dimensional bijective connection networks $B_{n}$ contain hypercubes, crossed cubes, M\u00f6bius cubes and twisted cubes, etc. The conditional edge-connectivity of a connected graph $G$ is the minimum cardinality of edge sets, whose deletion disconnects $G$ and results in each remaining component satisfying property $\\mathscr{P}$. And let $F$ be the edge set as desired. For a positive integer $a$, if $\\mathscr{P}$ denotes the property that the average degree of each component of $G-F$ is no less than $a$, then the conditional edge-connectivity can be called the $a$-average degree edge-connectivity $\\overline{\\lambda }_{a}(G)$. In this paper, we determine that the exact value of the $a$-average degree edge-connectivity of an $n$-dimensional bijective connection network $\\overline{\\lambda }_{a}(B_{n})$ is $(n-a)2^a$ for each $0\\leq a \\leq n-1 $ and $n\\geq 1$. 1<\/jats:p>","DOI":"10.1093\/comjnl\/bxac064","type":"journal-article","created":{"date-parts":[[2022,6,13]],"date-time":"2022-06-13T14:13:53Z","timestamp":1655129633000},"page":"2118-2122","source":"Crossref","is-referenced-by-count":5,"title":["The <i>a<\/i>-average Degree Edge-Connectivity of Bijective Connection Networks"],"prefix":"10.1093","volume":"66","author":[{"given":"Yayu","family":"Yang","sequence":"first","affiliation":[{"name":"College of Mathematics and System Sciences, Xinjiang University , Urumqi 830046 , China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Mingzu","family":"Zhang","sequence":"additional","affiliation":[{"name":"College of Mathematics and System Sciences, Xinjiang University , Urumqi 830046 , China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jixiang","family":"Meng","sequence":"additional","affiliation":[{"name":"College of Mathematics and System Sciences, Xinjiang University , Urumqi 830046 , China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Rongda","family":"Chen","sequence":"additional","affiliation":[{"name":"College of Mathematics and System Sciences, Xinjiang University , Urumqi 830046 , China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"286","published-online":{"date-parts":[[2022,6,12]]},"reference":[{"key":"2023091720460211300_ref1","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. 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