{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T12:59:29Z","timestamp":1740142769488,"version":"3.37.3"},"reference-count":14,"publisher":"Oxford University Press (OUP)","issue":"10","license":[{"start":{"date-parts":[[2022,7,30]],"date-time":"2022-07-30T00:00:00Z","timestamp":1659139200000},"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":["11671296"],"award-info":[{"award-number":["11671296"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2023,10,15]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>The problem of finding the maximum independent sets (or maximum cliques) of a given graph is fundamental in graph theory and is also one of the most important in terms of the application of graph theory. Let $A(n,d,w)$ be the size of the maximum independent set of $Q_{n}^{(d-1,w)}$, which is the induced subgraph of points of weight $w$ of the $d-1^{th}$-power of $n$-dimensional hypercubes. In order to further understand and study the dependent set of $Q_{n}^{(d-1,w)}$, we explore its clique number and the structure of the maximum clique. This paper obtains the clique number and the structure of the maximum clique of $Q_{n}^{(d-1,w)}$ for $5\\leq d\\leq 6$. Moreover, the characterizations for $A(n,d,w)=2$ and $3$ are also given.<\/jats:p>","DOI":"10.1093\/comjnl\/bxac103","type":"journal-article","created":{"date-parts":[[2022,7,29]],"date-time":"2022-07-29T20:10:00Z","timestamp":1659125400000},"page":"2535-2541","source":"Crossref","is-referenced-by-count":0,"title":["On The Maximum Cliques Of The Subgraphs Induced By Binary Constant Weight Codes In Powers Of Hypercubes"],"prefix":"10.1093","volume":"66","author":[{"given":"Juanjuan","family":"Shi","sequence":"first","affiliation":[{"name":"Department of Mathematics, Taiyuan University of Technology , Taiyuan Shanxi-030024 , China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yongfang","family":"Kou","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Taiyuan University of Technology , Taiyuan Shanxi-030024 , China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yulan","family":"Hu","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Taiyuan University of Technology , Taiyuan Shanxi-030024 , China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Weihua","family":"Yang","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Taiyuan University of Technology , Taiyuan Shanxi-030024 , China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"286","published-online":{"date-parts":[[2022,7,30]]},"reference":[{"key":"2023101421213531900_ref1","doi-asserted-by":"crossref","first-page":"323","DOI":"10.1109\/TC.1984.1676437","article-title":"Generalized hypercube and hyperbus structures for a computer network","volume":"33","author":"Bhuyan","year":"1984","journal-title":"IEEE Trans. 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J."},{"key":"2023101421213531900_ref8","doi-asserted-by":"crossref","first-page":"203","DOI":"10.1109\/TIT.1962.1057714","article-title":"A new upper bound for error-correcting codes","volume":"8","author":"Johnson","year":"1962","journal-title":"IEEE Transactions on Information Theory"},{"key":"2023101421213531900_ref9","doi-asserted-by":"crossref","first-page":"2373","DOI":"10.1109\/18.887851","article-title":"Upper bounds for constant-weight codes","volume":"46","author":"Agrell","year":"2000","journal-title":"IEEE Transactions on Information Theory"},{"key":"2023101421213531900_ref10","doi-asserted-by":"crossref","first-page":"1324","DOI":"10.1109\/18.45293","article-title":"New lower bounds for constant weight codes","volume":"35","author":"Cornelis","year":"1989","journal-title":"IEEE Transactions on Information Theory"},{"key":"2023101421213531900_ref11","doi-asserted-by":"crossref","first-page":"1334","DOI":"10.1109\/18.59932","article-title":"A new table of constant weight codes","volume":"36","author":"Brouwer","year":"1990","journal-title":"IEEE Transactions on Information Theory"},{"key":"2023101421213531900_ref12","doi-asserted-by":"crossref","first-page":"740","DOI":"10.12677\/AAM.2021.103081","article-title":"A note on A(n,d,w)","volume":"10","author":"Kou","year":"2021","journal-title":"Advances in Applied Mathematics"},{"key":"2023101421213531900_ref13","doi-asserted-by":"crossref","first-page":"466","DOI":"10.1109\/TIT.1971.1054656","article-title":"On upper bounds for unrestricted binary error-correcting code","volume":"17","author":"Johnson","year":"1971","journal-title":"IEEE Transactions on Information Theory"},{"key":"2023101421213531900_ref14","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4613-0163-9","volume-title":"Algebraic graph theory","author":"Godsil","year":"2001"}],"container-title":["The Computer Journal"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/academic.oup.com\/comjnl\/article-pdf\/66\/10\/2535\/52134777\/bxac103.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"https:\/\/academic.oup.com\/comjnl\/article-pdf\/66\/10\/2535\/52134777\/bxac103.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,10,14]],"date-time":"2023-10-14T21:22:31Z","timestamp":1697318551000},"score":1,"resource":{"primary":{"URL":"https:\/\/academic.oup.com\/comjnl\/article\/66\/10\/2535\/6651999"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,7,30]]},"references-count":14,"journal-issue":{"issue":"10","published-online":{"date-parts":[[2022,7,30]]},"published-print":{"date-parts":[[2023,10,15]]}},"URL":"https:\/\/doi.org\/10.1093\/comjnl\/bxac103","relation":{},"ISSN":["0010-4620","1460-2067"],"issn-type":[{"type":"print","value":"0010-4620"},{"type":"electronic","value":"1460-2067"}],"subject":[],"published-other":{"date-parts":[[2023,10]]},"published":{"date-parts":[[2022,7,30]]}}}