{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T16:39:05Z","timestamp":1740155945899,"version":"3.37.3"},"reference-count":27,"publisher":"World Scientific Pub Co Pte Ltd","issue":"03","funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11701218"],"award-info":[{"award-number":["11701218"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100003453","name":"Natural Science Foundation of Guangdong Province","doi-asserted-by":"publisher","award":["2016A030310082"],"award-info":[{"award-number":["2016A030310082"]}],"id":[{"id":"10.13039\/501100003453","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Tianyuan Fund of National Natural Science Foundation of China","award":["11626114"],"award-info":[{"award-number":["11626114"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Discrete Math. Algorithm. Appl."],"published-print":{"date-parts":[[2020,6]]},"abstract":"<jats:p> The folded hypercube is an important interconnection network for multiprocessor systems. Let [Formula: see text] with [Formula: see text] denote an [Formula: see text]-dimensional folded hypercube. For a given fault-free edge set [Formula: see text] with [Formula: see text] and a faulty edge set [Formula: see text] with [Formula: see text], in this paper we prove that [Formula: see text] contains a fault-free Hamiltonian cycle including each edge of [Formula: see text] if and only if the subgraph induced by [Formula: see text] is linear forest. Furthermore, we give the definitions of the distance among three vertex-disjoint edges and the distance between a vertex and a vertex set. For three vertex-disjoint edges [Formula: see text], the distance among them is denoted by [Formula: see text]. For a vertex [Formula: see text] and a vertex set [Formula: see text], the distance between [Formula: see text] and [Formula: see text] is denoted by [Formula: see text]. <\/jats:p>","DOI":"10.1142\/s1793830920500366","type":"journal-article","created":{"date-parts":[[2020,2,28]],"date-time":"2020-02-28T15:12:36Z","timestamp":1582902756000},"page":"2050036","source":"Crossref","is-referenced-by-count":0,"title":["Fault-free Hamiltonian cycle including given edges in folded hypercubes with faulty edges"],"prefix":"10.1142","volume":"12","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-9933-6601","authenticated-orcid":false,"given":"Dongqin","family":"Cheng","sequence":"first","affiliation":[{"name":"Department of Mathematics, Jinan University, No. 601, West Huangpu Avenue, Guangzhou, 510632, P. R. China"}]}],"member":"219","published-online":{"date-parts":[[2020,5,12]]},"reference":[{"key":"S1793830920500366BIB001","doi-asserted-by":"publisher","DOI":"10.1109\/TC.1984.1676437"},{"volume-title":"Graph Theory with Applications","year":"1980","author":"Bondy J. A.","key":"S1793830920500366BIB002"},{"key":"S1793830920500366BIB003","doi-asserted-by":"publisher","DOI":"10.1002\/jgt.20128"},{"key":"S1793830920500366BIB004","doi-asserted-by":"publisher","DOI":"10.1016\/j.disc.2005.12.050"},{"key":"S1793830920500366BIB005","doi-asserted-by":"publisher","DOI":"10.1007\/s00373-014-1426-0"},{"key":"S1793830920500366BIB006","doi-asserted-by":"publisher","DOI":"10.1016\/j.ipl.2007.06.014"},{"key":"S1793830920500366BIB007","doi-asserted-by":"publisher","DOI":"10.1016\/j.ipl.2011.10.010"},{"key":"S1793830920500366BIB008","first-page":"10058","volume":"217","author":"Chen H.-C.","year":"2011","journal-title":"Appl. Math. Comput."},{"issue":"4","key":"S1793830920500366BIB009","first-page":"662","volume":"4","author":"Chen J.-C.","year":"2010","journal-title":"Int. J. Comput. Inform. Eng."},{"key":"S1793830920500366BIB010","doi-asserted-by":"publisher","DOI":"10.1016\/j.dam.2017.12.014"},{"key":"S1793830920500366BIB011","doi-asserted-by":"publisher","DOI":"10.1137\/S0895480103432805"},{"key":"S1793830920500366BIB012","doi-asserted-by":"publisher","DOI":"10.1016\/j.disc.2005.12.045"},{"key":"S1793830920500366BIB013","doi-asserted-by":"publisher","DOI":"10.1109\/71.80187"},{"key":"S1793830920500366BIB014","doi-asserted-by":"publisher","DOI":"10.1016\/j.ipl.2008.07.015"},{"key":"S1793830920500366BIB015","doi-asserted-by":"publisher","DOI":"10.1016\/j.ins.2014.08.019"},{"key":"S1793830920500366BIB016","doi-asserted-by":"publisher","DOI":"10.1016\/j.ipl.2008.02.013"},{"volume-title":"Introduction to Parallel Algorithms and Architecture: Arrays, Trees, Hypercubes","year":"1992","author":"Leighton F. T.","key":"S1793830920500366BIB017"},{"key":"S1793830920500366BIB018","doi-asserted-by":"publisher","DOI":"10.1016\/S0020-0190(03)00258-8"},{"key":"S1793830920500366BIB019","doi-asserted-by":"publisher","DOI":"10.1016\/j.dam.2013.07.004"},{"key":"S1793830920500366BIB020","first-page":"103","volume":"21","author":"Simmons G.","year":"1978","journal-title":"Congressus Numerantium."},{"key":"S1793830920500366BIB021","doi-asserted-by":"publisher","DOI":"10.1016\/j.tcs.2004.01.035"},{"key":"S1793830920500366BIB022","doi-asserted-by":"publisher","DOI":"10.1016\/j.aml.2008.08.021"},{"key":"S1793830920500366BIB023","doi-asserted-by":"publisher","DOI":"10.1016\/S0020-0190(02)00214-4"},{"key":"S1793830920500366BIB024","doi-asserted-by":"publisher","DOI":"10.1016\/j.ipl.2008.02.016"},{"key":"S1793830920500366BIB025","first-page":"7","volume":"35","author":"Xu J.-M.","year":"2006","journal-title":"Australasian J. Comb."},{"key":"S1793830920500366BIB026","doi-asserted-by":"publisher","DOI":"10.1016\/j.dam.2016.12.006"},{"key":"S1793830920500366BIB027","doi-asserted-by":"publisher","DOI":"10.1109\/TPDS.2014.2311794"}],"container-title":["Discrete Mathematics, Algorithms and Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S1793830920500366","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,7,8]],"date-time":"2020-07-08T10:50:11Z","timestamp":1594205411000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S1793830920500366"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,5,12]]},"references-count":27,"journal-issue":{"issue":"03","published-print":{"date-parts":[[2020,6]]}},"alternative-id":["10.1142\/S1793830920500366"],"URL":"https:\/\/doi.org\/10.1142\/s1793830920500366","relation":{},"ISSN":["1793-8309","1793-8317"],"issn-type":[{"type":"print","value":"1793-8309"},{"type":"electronic","value":"1793-8317"}],"subject":[],"published":{"date-parts":[[2020,5,12]]}}}