{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,3,29]],"date-time":"2022-03-29T00:26:42Z","timestamp":1648513602733},"reference-count":22,"publisher":"World Scientific Pub Co Pte Lt","issue":"01","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Discrete Math. Algorithm. Appl."],"published-print":{"date-parts":[[2016,3]]},"abstract":"<jats:p> The folded hypercube is a well-known variation of hypercube structure and can be constructed from a hypercube by adding an edge to every pair of vertices with complementary addresses. Let [Formula: see text] (respectively, [Formula: see text]) denote the set of faulty vertices (respectively, faulty edges) in an [Formula: see text]-dimensional folded hypercube [Formula: see text]. In the case that all edges in [Formula: see text] are fault-free, Cheng et\u00a0al. [Cycles embedding on folded hypercubes with faulty vertices, Discrete Appl. Math. 161 (2013) 2894\u20132900] has shown that (1) every fault-free edge of [Formula: see text] lies on a fault-free cycle of every even length from [Formula: see text] to [Formula: see text] if [Formula: see text], where [Formula: see text]; and (2) every fault-free edge of [Formula: see text] lies on a fault-free cycle of every odd length from [Formula: see text] to [Formula: see text] if [Formula: see text], where [Formula: see text] is even. In this paper, we extend Cheng\u2019s result to obtain two further properties, which consider both vertex and edge faults, as follows: <\/jats:p><jats:p> (1) Every fault-free edge of [Formula: see text] lies on a fault-free cycle of every even length from [Formula: see text] to [Formula: see text] if [Formula: see text], where [Formula: see text]; <\/jats:p><jats:p> (2) Every fault-free edge of [Formula: see text] lies on a fault-free cycle of every odd length from [Formula: see text] to [Formula: see text] if [Formula: see text], where [Formula: see text] is even. <\/jats:p>","DOI":"10.1142\/s1793830916500014","type":"journal-article","created":{"date-parts":[[2015,10,27]],"date-time":"2015-10-27T07:11:52Z","timestamp":1445929912000},"page":"1650001","source":"Crossref","is-referenced-by-count":0,"title":["Every edge lies on cycles embedding in folded hypercubes with both vertex and edge faults"],"prefix":"10.1142","volume":"08","author":[{"given":"Che-Nan","family":"Kuo","sequence":"first","affiliation":[{"name":"Department of Animation and Game Design, Toko University, No. 51, Sec. 2, Xuefu Road, Puzi City, ChiaYi County 61363, Taiwan"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2016,2,26]]},"reference":[{"key":"S1793830916500014BIB002","doi-asserted-by":"publisher","DOI":"10.1016\/j.dam.2013.06.030"},{"key":"S1793830916500014BIB003","doi-asserted-by":"publisher","DOI":"10.1109\/71.80187"},{"key":"S1793830916500014BIB004","doi-asserted-by":"publisher","DOI":"10.1109\/12.67323"},{"key":"S1793830916500014BIB005","doi-asserted-by":"publisher","DOI":"10.1016\/j.ipl.2008.05.024"},{"key":"S1793830916500014BIB006","doi-asserted-by":"publisher","DOI":"10.1002\/net.20204"},{"key":"S1793830916500014BIB007","doi-asserted-by":"publisher","DOI":"10.1016\/j.ipl.2008.04.003"},{"key":"S1793830916500014BIB008","doi-asserted-by":"publisher","DOI":"10.1002\/1097-0037(200012)36:4<225::AID-NET3>3.0.CO;2-G"},{"key":"S1793830916500014BIB009","doi-asserted-by":"publisher","DOI":"10.1016\/j.camwa.2006.10.033"},{"key":"S1793830916500014BIB010","doi-asserted-by":"publisher","DOI":"10.1016\/j.ipl.2009.10.003"},{"key":"S1793830916500014BIB011","doi-asserted-by":"publisher","DOI":"10.1016\/j.dam.2009.06.012"},{"key":"S1793830916500014BIB012","doi-asserted-by":"publisher","DOI":"10.1016\/j.dam.2007.08.043"},{"key":"S1793830916500014BIB013","doi-asserted-by":"publisher","DOI":"10.1016\/j.tcs.2012.11.028"},{"key":"S1793830916500014BIB014","doi-asserted-by":"publisher","DOI":"10.1016\/j.ins.2010.04.003"},{"key":"S1793830916500014BIB015","volume-title":"Introduction Parallel Algorithms and Architecture: Arrays, Trees, Hypercubes","author":"Leighton F. 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