{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T01:21:40Z","timestamp":1760145700787,"version":"build-2065373602"},"reference-count":28,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2024,8,18]],"date-time":"2024-08-18T00:00:00Z","timestamp":1723939200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100018585","name":"Xinjiang Tianchi Doctoral Project, China","doi-asserted-by":"publisher","award":["5105240150c","QZX20240031"],"award-info":[{"award-number":["5105240150c","QZX20240031"]}],"id":[{"id":"10.13039\/501100018585","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Foundation of China University of Petroleum, Beijing, at Karamay","award":["5105240150c","QZX20240031"],"award-info":[{"award-number":["5105240150c","QZX20240031"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>Embedding cycles into a network topology is crucial for a network simulation. In particular, embedding Hamiltonian cycles is a major requirement for designing good interconnection networks. A graph G is called r-spanning cyclable if, for any r distinct vertices v1,v2,\u2026,vr of G, there exist r cycles C1,C2,\u2026,Cr in G such that vi is on Ci for every i, and every vertex of G is on exactly one cycle Ci. If r=1, this is the classical Hamiltonian problem. In this paper, we focus on the problem of embedding spanning disjoint cycles in bipartite k-ary n-cubes. Let k\u22654 be even and n\u22652. It is shown that the n-dimensional bipartite k-ary n-cube Qnk is m-spanning cyclable with m\u22642n\u22121. Considering the degree of Qnk, the result is optimal.<\/jats:p>","DOI":"10.3390\/sym16081063","type":"journal-article","created":{"date-parts":[[2024,8,19]],"date-time":"2024-08-19T03:43:28Z","timestamp":1724039008000},"page":"1063","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["On the Spanning Cyclability of k-ary n-cube Networks"],"prefix":"10.3390","volume":"16","author":[{"given":"Hongwei","family":"Qiao","sequence":"first","affiliation":[{"name":"College of Mathematics and System Sciences, Xinjiang University, Urumqi 830046, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Wanping","family":"Zhang","sequence":"additional","affiliation":[{"name":"Department of Mathematics, School of Science and Art, China University of Petroleum-Beijing at Karamay, Karamay 834000, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2024,8,18]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Leighton, F.T. 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