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Lett."],"published-print":{"date-parts":[[2020,9]]},"abstract":"<jats:p>The [Formula: see text]-extra conditional diagnosability and [Formula: see text]-extra connectivity are two important parameters to measure ability of diagnosing faulty processors and fault tolerance in a multiprocessor system. The [Formula: see text]-extra conditional diagnosability [Formula: see text] of graph [Formula: see text] is defined as the diagnosability of a multiprocessor system under the assumption that every fault-free component contains more than [Formula: see text] vertices. While the [Formula: see text]-extra connectivity [Formula: see text] of graph [Formula: see text] is the minimum number [Formula: see text] for which there is a vertex cut [Formula: see text] with [Formula: see text] such that every component of [Formula: see text] has more than [Formula: see text] vertices. In this paper, we study the [Formula: see text]-extra conditional diagnosability of graph [Formula: see text] in terms of its [Formula: see text]-extra connectivity, and show that [Formula: see text] under the MM* model with some acceptable conditions. As applications, the [Formula: see text]-extra conditional diagnosability is determined for some BC networks such as hypercubes, varietal hypercubes, and [Formula: see text]-ary [Formula: see text]-cubes under the MM* model.<\/jats:p>","DOI":"10.1142\/s012962642040006x","type":"journal-article","created":{"date-parts":[[2020,10,13]],"date-time":"2020-10-13T07:38:43Z","timestamp":1602574723000},"page":"2040006","source":"Crossref","is-referenced-by-count":6,"title":["The<i>g<\/i>-Extra Conditional Diagnosability of Graphs in Terms of<i>g<\/i>-Extra Connectivity"],"prefix":"10.1142","volume":"30","author":[{"given":"Aixia","family":"Liu","sequence":"first","affiliation":[{"name":"School of Applied Sciences, Taiyuan University of Science and Technology, Taiyuan 030024, People\u2019s Republic of China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5918-7960","authenticated-orcid":false,"given":"Jun","family":"Yuan","sequence":"additional","affiliation":[{"name":"School of Applied Sciences, Taiyuan University of Science and Technology, Taiyuan 030024, People\u2019s Republic of China"}]},{"given":"Shiying","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Mathematics and Computer Science, Shanxi Normal University, Linfen 041004, People\u2019s Republic of China"}]}],"member":"219","published-online":{"date-parts":[[2020,10,12]]},"reference":[{"key":"S012962642040006XBIB001","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-349-03521-2"},{"key":"S012962642040006XBIB002","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcss.2013.01.013"},{"key":"S012962642040006XBIB003","doi-asserted-by":"publisher","DOI":"10.1109\/TC.2010.201"},{"key":"S012962642040006XBIB004","doi-asserted-by":"publisher","DOI":"10.1016\/j.amc.2006.11.085"},{"key":"S012962642040006XBIB005","doi-asserted-by":"crossref","first-page":"13","DOI":"10.1142\/S0219265904001003","volume":"5","author":"Day K.","year":"2004","journal-title":"J. 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