{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,23]],"date-time":"2025-09-23T14:18:43Z","timestamp":1758637123283},"reference-count":18,"publisher":"EDP Sciences","issue":"3-4","license":[{"start":{"date-parts":[[2019,10,24]],"date-time":"2019-10-24T00:00:00Z","timestamp":1571875200000},"content-version":"vor","delay-in-days":115,"URL":"https:\/\/www.edpsciences.org\/en\/authors\/copyright-and-licensing"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["RAIRO-Theor. Inf. Appl."],"accepted":{"date-parts":[[2019,7,3]]},"published-print":{"date-parts":[[2019,7]]},"abstract":"<jats:p>The class of <jats:italic>k<\/jats:italic>-ary <jats:italic>n<\/jats:italic>-cubes represents the most commonly used interconnection topology for parallel and distributed computing systems. In this paper, we consider the faulty <jats:italic>k<\/jats:italic>-ary <jats:italic>n<\/jats:italic>-cube with even <jats:italic>k<\/jats:italic> \u2265 4 and <jats:italic>n<\/jats:italic> \u2265 2 such that each vertex of the <jats:italic>k<\/jats:italic>-ary <jats:italic>n<\/jats:italic>-cube is incident with at least two healthy edges. Based on this requirement, we investigate the fault-tolerant capabilities of the <jats:italic>k<\/jats:italic>-ary <jats:italic>n<\/jats:italic>-cube with respect to the edge-bipancyclicity. We prove that in the <jats:italic>k<\/jats:italic>-ary <jats:italic>n<\/jats:italic>-cube <jats:italic>Q<jats:sub>n<\/jats:sub><jats:sup>k<\/jats:sup><\/jats:italic>, every healthy edge is contained in fault-free cycles of even lengths from 6 to |<jats:italic>V<\/jats:italic>(<jats:italic>Q<jats:sub>n<\/jats:sub><jats:sup>k<\/jats:sup><\/jats:italic>)|, even if the <jats:italic>Q<jats:sub>n<\/jats:sub><jats:sup>k<\/jats:sup><\/jats:italic> has up to 4<jats:italic>n<\/jats:italic> \u2212 5 edge faults and our result is optimal with respect to the number of edge faults tolerated.<\/jats:p>","DOI":"10.1051\/ita\/2019003","type":"journal-article","created":{"date-parts":[[2019,10,24]],"date-time":"2019-10-24T12:33:03Z","timestamp":1571920383000},"page":"85-113","source":"Crossref","is-referenced-by-count":1,"title":["Edge-bipancyclicity in conditional edge-faulty <i>k<\/i>-ary <i>n<\/i>-cubes"],"prefix":"10.1051","volume":"53","author":[{"given":"Shiying","family":"Wang","sequence":"first","affiliation":[]},{"given":"Shurong","family":"Zhang","sequence":"additional","affiliation":[]}],"member":"250","published-online":{"date-parts":[[2019,10,24]]},"reference":[{"key":"R1","doi-asserted-by":"crossref","first-page":"265","DOI":"10.1147\/rd.492.0265","volume":"49","author":"Adiga","year":"2005","journal-title":"IBM J. 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