{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,3,30]],"date-time":"2022-03-30T19:49:45Z","timestamp":1648669785347},"reference-count":15,"publisher":"World Scientific Pub Co Pte Lt","issue":"02","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. Inter. Net."],"published-print":{"date-parts":[[2021,6]]},"abstract":"<jats:p> Let [Formula: see text] be a connected graph with minimum degree at least [Formula: see text] and let [Formula: see text] be an integer such that [Formula: see text] The conditional [Formula: see text]-edge ([Formula: see text]-vertex) cut of [Formula: see text] is defined as a set [Formula: see text] of edges (vertices) of [Formula: see text] whose removal disconnects [Formula: see text] leaving behind components of minimum degree at least [Formula: see text] The characterization of a minimum [Formula: see text]-vertex cut of the [Formula: see text]-dimensional hypercube [Formula: see text] is known. In this paper, we characterize a minimum [Formula: see text]-edge cut of [Formula: see text] Also, we obtain a sharp lower bound on the number of vertices of an [Formula: see text]-edge cut of [Formula: see text] and obtain some consequences. <\/jats:p>","DOI":"10.1142\/s0219265921500079","type":"journal-article","created":{"date-parts":[[2021,6,4]],"date-time":"2021-06-04T16:35:24Z","timestamp":1622824524000},"page":"2150007","source":"Crossref","is-referenced-by-count":0,"title":["A Note on Conditional Edge Connectivity of Hypercube Networks"],"prefix":"10.1142","volume":"21","author":[{"given":"J. B.","family":"Saraf","sequence":"first","affiliation":[{"name":"Department of Mathematics, Savitribai Phule Pune Univeristy, Pune 411007, India"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Y. M.","family":"Borse","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Savitribai Phule Pune Univeristy, Pune 411007, India"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2021,7,18]]},"reference":[{"key":"S0219265921500079BIB001","doi-asserted-by":"publisher","DOI":"10.1142\/S179383091750032X"},{"key":"S0219265921500079BIB002","doi-asserted-by":"publisher","DOI":"10.1142\/S1793830915500330"},{"key":"S0219265921500079BIB003","first-page":"221","volume":"80","author":"Borse Y. M.","year":"2013","journal-title":"J. Indian Math. Soc."},{"key":"S0219265921500079BIB004","doi-asserted-by":"publisher","DOI":"10.1006\/jctb.1997.1775"},{"key":"S0219265921500079BIB005","doi-asserted-by":"publisher","DOI":"10.1002\/net.3230130303"},{"key":"S0219265921500079BIB006","doi-asserted-by":"publisher","DOI":"10.1109\/12.262126"},{"key":"S0219265921500079BIB007","volume-title":"Introduction to Parallel Algorithms and Architectures: Arrays, Trees, Hypercube","author":"Leighton F. T.","year":"1992"},{"key":"S0219265921500079BIB008","doi-asserted-by":"publisher","DOI":"10.1016\/j.ipl.2013.07.010"},{"key":"S0219265921500079BIB009","doi-asserted-by":"publisher","DOI":"10.1109\/71.242153"},{"key":"S0219265921500079BIB010","doi-asserted-by":"publisher","DOI":"10.1016\/j.disc.2004.08.010"},{"key":"S0219265921500079BIB011","author":"Saraf J. B.","year":"2020","journal-title":"Discuss. Math. Graph Theory"},{"key":"S0219265921500079BIB012","doi-asserted-by":"publisher","DOI":"10.1142\/S0219265920500139"},{"key":"S0219265921500079BIB013","doi-asserted-by":"publisher","DOI":"10.1007\/BF02671131"},{"key":"S0219265921500079BIB014","doi-asserted-by":"publisher","DOI":"10.1016\/j.aml.2011.11.040"},{"key":"S0219265921500079BIB015","doi-asserted-by":"publisher","DOI":"10.1049\/cje.2016.05.023"}],"container-title":["Journal of Interconnection Networks"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0219265921500079","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,7,21]],"date-time":"2021-07-21T09:28:44Z","timestamp":1626859724000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0219265921500079"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,6]]},"references-count":15,"journal-issue":{"issue":"02","published-print":{"date-parts":[[2021,6]]}},"alternative-id":["10.1142\/S0219265921500079"],"URL":"https:\/\/doi.org\/10.1142\/s0219265921500079","relation":{},"ISSN":["0219-2659","1793-6713"],"issn-type":[{"value":"0219-2659","type":"print"},{"value":"1793-6713","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,6]]}}}