{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,5]],"date-time":"2022-04-05T09:44:44Z","timestamp":1649151884998},"reference-count":23,"publisher":"World Scientific Pub Co Pte Lt","issue":"04","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. Inter. Net."],"published-print":{"date-parts":[[2011,12]]},"abstract":"<jats:p> In this paper, we consider the conditionally faulty graphs G that each vertex of G is incident with at least m fault-free edges, 2 \u2264 m \u2264 n - 1. We extend the limitation m \u2265 2 in all previous results of edge-bipancyclicity with faulty edges and faulty vertices. Let f<jats:sub>e<\/jats:sub> (respectively, f<jats:sub>v<\/jats:sub>) denotes the number of faulty edges (respectively, faulty vertices) in an n-dimensional hypercube Q<jats:sub>n<\/jats:sub>. For all m, we show that every fault-free edge of Q<jats:sub>n<\/jats:sub> lies on a fault-free cycle of every even length from 4 to |V| - 2f<jats:sub>v<\/jats:sub> inclusive provided f<jats:sub>e<\/jats:sub> + f<jats:sub>v<\/jats:sub> \u2264 n - 2. This result is not only optimal, but also improves on the previously best known results reported in the literature. <\/jats:p>","DOI":"10.1142\/s0219265911003039","type":"journal-article","created":{"date-parts":[[2012,6,27]],"date-time":"2012-06-27T17:55:12Z","timestamp":1340819712000},"page":"337-343","source":"Crossref","is-referenced-by-count":1,"title":["EDGE-BIPANCYCLICITY OF HYPERCUBES WITH CONDITIONAL FAULTS"],"prefix":"10.1142","volume":"12","author":[{"given":"CHAO-MING","family":"SUN","sequence":"first","affiliation":[{"name":"Department of Electrical Engineering, R.O.C. Military Academy, Kaohsiung 83059, Taiwan"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2012,6,28]]},"reference":[{"key":"rf1","doi-asserted-by":"publisher","DOI":"10.1016\/0012-365X(91)90417-Z"},{"key":"rf2","volume-title":"Graph Theory with Applications","author":"Bondy J. A.","year":"1980"},{"key":"rf3","doi-asserted-by":"publisher","DOI":"10.1016\/0095-8956(71)90016-5"},{"key":"rf4","doi-asserted-by":"publisher","DOI":"10.1137\/0404045"},{"key":"rf5","doi-asserted-by":"publisher","DOI":"10.1109\/TCOMM.2011.093011.100321"},{"key":"rf6","doi-asserted-by":"publisher","DOI":"10.1016\/S0167-8191(03)00058-9"},{"key":"rf7","doi-asserted-by":"publisher","DOI":"10.1016\/0095-8956(76)90061-7"},{"key":"rf8","first-page":"2010","volume":"23","author":"Hsieh S. Y.","journal-title":"SIAM J. Discrete Math."},{"key":"rf9","doi-asserted-by":"publisher","DOI":"10.1109\/TPDS.2008.123"},{"key":"rf10","doi-asserted-by":"publisher","DOI":"10.1109\/TC.2006.104"},{"key":"rf11","doi-asserted-by":"crossref","DOI":"10.1201\/9781420044829","volume-title":"Graph theory and interconnection networks","author":"Hsu L. H.","year":"2008"},{"key":"rf12","volume-title":"Introduction to Parallel Algorithms and Architectures: Arrays \u00b7 Trees \u00b7 Hypercubes","author":"Leighton F. T.","year":"1992"},{"key":"rf13","doi-asserted-by":"publisher","DOI":"10.1016\/S0020-0190(03)00258-8"},{"key":"rf14","first-page":"271","author":"Mitchem J.","journal-title":"Graphs and Applications"},{"key":"rf15","doi-asserted-by":"publisher","DOI":"10.1109\/12.2234"},{"key":"rf16","doi-asserted-by":"publisher","DOI":"10.1016\/j.ipl.2007.07.009"},{"key":"rf17","doi-asserted-by":"publisher","DOI":"10.1016\/j.amc.2011.11.041"},{"key":"rf19","doi-asserted-by":"publisher","DOI":"10.1142\/S0219265907001941"},{"key":"rf20","doi-asserted-by":"publisher","DOI":"10.1016\/j.ins.2007.06.013"},{"key":"rf21","doi-asserted-by":"publisher","DOI":"10.1016\/j.ipl.2006.12.016"},{"key":"rf22","doi-asserted-by":"publisher","DOI":"10.1016\/j.tcs.2004.01.035"},{"key":"rf23","doi-asserted-by":"publisher","DOI":"10.1016\/j.ipl.2005.06.006"},{"key":"rf24","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4757-3387-7"}],"container-title":["Journal of Interconnection Networks"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0219265911003039","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,7]],"date-time":"2019-08-07T17:08:53Z","timestamp":1565197733000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0219265911003039"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2011,12]]},"references-count":23,"journal-issue":{"issue":"04","published-online":{"date-parts":[[2012,6,28]]},"published-print":{"date-parts":[[2011,12]]}},"alternative-id":["10.1142\/S0219265911003039"],"URL":"https:\/\/doi.org\/10.1142\/s0219265911003039","relation":{},"ISSN":["0219-2659","1793-6713"],"issn-type":[{"value":"0219-2659","type":"print"},{"value":"1793-6713","type":"electronic"}],"subject":[],"published":{"date-parts":[[2011,12]]}}}