{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T02:45:58Z","timestamp":1760150758809,"version":"build-2065373602"},"reference-count":31,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2023,12,28]],"date-time":"2023-12-28T00:00:00Z","timestamp":1703721600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/100007834","name":"Ningbo Natural Science Foundation","doi-asserted-by":"publisher","award":["2023J186","Y202351606","2090011540015"],"award-info":[{"award-number":["2023J186","Y202351606","2090011540015"]}],"id":[{"id":"10.13039\/100007834","id-type":"DOI","asserted-by":"publisher"}]},{"name":"General Scientific Research Foundation of Zhejiang Province Education Department","award":["2023J186","Y202351606","2090011540015"],"award-info":[{"award-number":["2023J186","Y202351606","2090011540015"]}]},{"name":"Ph.D. Research Startup Foundation of Ningbo University of Technology","award":["2023J186","Y202351606","2090011540015"],"award-info":[{"award-number":["2023J186","Y202351606","2090011540015"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>The enhanced hypercube is a well-known variant of the hypercube and can be constructed from a hypercube by adding an edge to every pair of vertices with complementary addresses. Let Fv denote the set of faulty vertices in an n-dimensional enhanced hypercube Qn,k(1\u2264k\u2264n\u22121). In this paper, we conclude that if n\u22652, then every fault-free edge of Qn,k\u2212Fv lies on a fault-free cycle of every even length from 4 to 2n\u22122|Fv|, and if n(\u22652) and k have the different parity, then every fault-free edge of Qn,k\u2212Fv lies on a fault-free cycle of every possible odd length from n\u2212k+4 to 2n\u22122|Fv|\u22121, where |Fv|\u2264n\u22122.<\/jats:p>","DOI":"10.3390\/sym16010044","type":"journal-article","created":{"date-parts":[[2023,12,28]],"date-time":"2023-12-28T11:44:57Z","timestamp":1703763897000},"page":"44","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Cycle Embedding in Enhanced Hypercubes with Faulty Vertices"],"prefix":"10.3390","volume":"16","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-1317-8935","authenticated-orcid":false,"given":"Min","family":"Liu","sequence":"first","affiliation":[{"name":"School of Science, Ningbo University of Technology, Ningbo 315211, China"}]}],"member":"1968","published-online":{"date-parts":[[2023,12,28]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Leighton, F.T. 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