{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,16]],"date-time":"2026-03-16T08:53:40Z","timestamp":1773651220251,"version":"3.50.1"},"reference-count":25,"publisher":"World Scientific Pub Co Pte Ltd","issue":"03","funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61772010"],"award-info":[{"award-number":["61772010"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Shanxi Provincial Fundamental Research Program of China","award":["202203021221128"],"award-info":[{"award-number":["202203021221128"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Found. Comput. Sci."],"published-print":{"date-parts":[[2026,4]]},"abstract":"<jats:p>The modified bubble-sort network is a famous Cayley graph model, which has strong symmetry and recursive structure, as well as good topological structure and properties. The cycle embedding problem is widely discussed in many networks, and edge fault tolerance is an important issue for networks since edge failures may occur when a network is put into use. In this paper, we prove that for any edge subset F of the n-dimensional modified bubble-sort graph [Formula: see text], every edge of [Formula: see text] lies on a cycle of every even length from [Formula: see text] to [Formula: see text] when [Formula: see text] does not exceed [Formula: see text]. As a corollary, the cycles of every even length from 4 to [Formula: see text] can be embedded into the n-dimensional modified bubble-sort graph when the number of fault edges in the graph does not exceed [Formula: see text].<\/jats:p>","DOI":"10.1142\/s0129054125500182","type":"journal-article","created":{"date-parts":[[2025,5,13]],"date-time":"2025-05-13T02:45:16Z","timestamp":1747104316000},"page":"467-484","source":"Crossref","is-referenced-by-count":0,"title":["Edge-Fault-Tolerant Edge-Bipancyclicity of Modified Bubble-Sort Graphs"],"prefix":"10.1142","volume":"37","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-9335-3005","authenticated-orcid":false,"given":"Shiying","family":"Wang","sequence":"first","affiliation":[{"name":"School of Mathematics and Computer Science, Shanxi Normal University, Taiyuan, Shanxi 030031, P. R. China"}]},{"ORCID":"https:\/\/orcid.org\/0009-0004-6892-3554","authenticated-orcid":false,"given":"Huiying","family":"Zhang","sequence":"additional","affiliation":[{"name":"School of Mathematics and Computer Science, Shanxi Normal University, Taiyuan, Shanxi 030031, P. R. China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8467-2370","authenticated-orcid":false,"given":"Lina","family":"Zhao","sequence":"additional","affiliation":[{"name":"School of Mathematics and Computer Science, Shanxi Normal University, Taiyuan, Shanxi 030031, P. R. China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0588-7857","authenticated-orcid":false,"given":"Shangwei","family":"Lin","sequence":"additional","affiliation":[{"name":"School of Mathematical Sciences, Shanxi University, Taiyuan, Shanxi 030006, P. R. China"}]}],"member":"219","published-online":{"date-parts":[[2025,5,13]]},"reference":[{"key":"S0129054125500182BIB001","first-page":"140","volume":"4","author":"Abdallah M.","year":"2019","journal-title":"Int. J. Comput. Mathematics: Comput. Syst. Theory"},{"key":"S0129054125500182BIB002","doi-asserted-by":"publisher","DOI":"10.1109\/12.21148"},{"key":"S0129054125500182BIB003","first-page":"80","volume":"11","author":"Bondy J. A.","year":"1971","journal-title":"Graph Theory and Computing"},{"key":"S0129054125500182BIB004","unstructured":"F. Buckley and  F. Harary,  Distance in Graphs (Addison-Wesley,  Reading, MA,  1989), pp. 283\u2013296."},{"key":"S0129054125500182BIB005","doi-asserted-by":"publisher","DOI":"10.1016\/j.dam.2021.10.012"},{"key":"S0129054125500182BIB006","doi-asserted-by":"publisher","DOI":"10.1016\/0095-8956(76)90061-7"},{"issue":"7","key":"S0129054125500182BIB007","volume":"34","author":"Islam N. R.","year":"2023","journal-title":"Int. J. Found. Comput. Sci."},{"key":"S0129054125500182BIB008","doi-asserted-by":"publisher","DOI":"10.1016\/j.ipl.2006.05.012"},{"key":"S0129054125500182BIB009","doi-asserted-by":"publisher","DOI":"10.1016\/j.tcs.2016.02.029"},{"key":"S0129054125500182BIB010","doi-asserted-by":"publisher","DOI":"10.1016\/0167-8191(93)90054-O"},{"key":"S0129054125500182BIB011","doi-asserted-by":"publisher","DOI":"10.1142\/S0129054121500039"},{"key":"S0129054125500182BIB012","doi-asserted-by":"publisher","DOI":"10.1016\/j.tcs.2020.09.042"},{"issue":"5","key":"S0129054125500182BIB013","first-page":"25","volume":"30","author":"Li P.","year":"2019","journal-title":"faults, Int. J. Found. Comput. Sci."},{"key":"S0129054125500182BIB014","doi-asserted-by":"publisher","DOI":"10.1016\/j.tcs.2018.08.017"},{"key":"S0129054125500182BIB015","doi-asserted-by":"publisher","DOI":"10.1016\/j.tcs.2023.113860"},{"key":"S0129054125500182BIB016","doi-asserted-by":"publisher","DOI":"10.1016\/j.dam.2022.12.005"},{"key":"S0129054125500182BIB017","doi-asserted-by":"publisher","DOI":"10.1016\/j.ipl.2021.106160"},{"key":"S0129054125500182BIB018","author":"Shi H.","year":"2011","journal-title":"Mathematics in Practice Theory"},{"key":"S0129054125500182BIB019","doi-asserted-by":"publisher","DOI":"10.1016\/j.amc.2022.127257"},{"key":"S0129054125500182BIB020","doi-asserted-by":"publisher","DOI":"10.1016\/j.amc.2020.125305"},{"key":"S0129054125500182BIB021","doi-asserted-by":"publisher","DOI":"10.3390\/axioms12090861"},{"key":"S0129054125500182BIB022","doi-asserted-by":"publisher","DOI":"10.1007\/s10114-011-0511-z"},{"key":"S0129054125500182BIB023","doi-asserted-by":"publisher","DOI":"10.1016\/j.tcs.2016.03.001"},{"key":"S0129054125500182BIB024","doi-asserted-by":"publisher","DOI":"10.1016\/j.ins.2013.04.011"},{"key":"S0129054125500182BIB025","doi-asserted-by":"publisher","DOI":"10.1142\/S0129054117500058"}],"container-title":["International Journal of Foundations of Computer Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0129054125500182","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,3,16]],"date-time":"2026-03-16T08:06:22Z","timestamp":1773648382000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/10.1142\/S0129054125500182"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,5,13]]},"references-count":25,"journal-issue":{"issue":"03","published-print":{"date-parts":[[2026,4]]}},"alternative-id":["10.1142\/S0129054125500182"],"URL":"https:\/\/doi.org\/10.1142\/s0129054125500182","relation":{},"ISSN":["0129-0541","1793-6373"],"issn-type":[{"value":"0129-0541","type":"print"},{"value":"1793-6373","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,5,13]]}}}