{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T19:10:14Z","timestamp":1760123414487,"version":"build-2065373602"},"reference-count":19,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2023,2,13]],"date-time":"2023-02-13T00:00:00Z","timestamp":1676246400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Information"],"abstract":"<jats:p>As two significant performance indicators, structure connectivity and substructure connectivity have been widely studied, and they are used to judge a network\u2019s fault tolerance properties from the perspective of the structure becoming faulty. An n-dimensional bubble-sort star graph BSn is a popular interconnection network with many good properties. We find the upper bounds of \u03ba(BSn;K1,3) and \u03bas(BSn;K1,3) in this paper. Furthermore, we establish \u03ba(BSn;H) and \u03bas(BSn;H) of BSn, where H\u2208{K1,K1,1,K1,2}.<\/jats:p>","DOI":"10.3390\/info14020120","type":"journal-article","created":{"date-parts":[[2023,2,14]],"date-time":"2023-02-14T01:41:06Z","timestamp":1676338866000},"page":"120","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Structure Fault Tolerance of Bubble-Sort Star Graphs"],"prefix":"10.3390","volume":"14","author":[{"given":"Lantao","family":"You","sequence":"first","affiliation":[{"name":"School of Information Engineering, Suzhou Industrial Park Institute of Services Outsourcing, Suzhou 215123, China"},{"name":"Provincial Key Laboratory for Computer Information Processing Technology, Soochow University, Suzhou 215006, China"},{"name":"School of Computer Science and Technology, Soochow University, Suzhou 215006, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jianfeng","family":"Jiang","sequence":"additional","affiliation":[{"name":"School of Information Engineering, Suzhou Industrial Park Institute of Services Outsourcing, Suzhou 215123, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yuejuan","family":"Han","sequence":"additional","affiliation":[{"name":"School of Computer Science and Technology, Soochow University, Suzhou 215006, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,2,13]]},"reference":[{"key":"ref_1","unstructured":"West, D.B. (2001). Introduction to Graph Theory, Prentice Hall Publishers."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"C347","DOI":"10.1002\/net.3230130303","article-title":"Conditional connectivity","volume":"13","author":"Harary","year":"1983","journal-title":"Networks"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"C49","DOI":"10.1016\/0012-365X(94)00369-T","article-title":"On the extraconnectivity of graphs","volume":"155","author":"Fabrega","year":"1996","journal-title":"Discret. Math."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"195","DOI":"10.1016\/0020-0190(88)90025-7","article-title":"On computing a conditional edge-connectivity of a graph","volume":"27","author":"Esfahanian","year":"1988","journal-title":"Inform. Process. Lett."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"1586","DOI":"10.1109\/12.42131","article-title":"Generalized measures of fault tolerance with application to n-cube networks","volume":"38","author":"Esfahanian","year":"1989","journal-title":"IEEE Trans. Comput."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"218","DOI":"10.1109\/12.262126","article-title":"Conditional connectivity measures for large multiprocessor systems","volume":"43","author":"Latifi","year":"1994","journal-title":"IEEE Trans. Comput."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"97","DOI":"10.1016\/j.tcs.2016.04.014","article-title":"Structure connectivity and substructure connectivity of hypercubes","volume":"634","author":"Lin","year":"2016","journal-title":"Theor. Comput. Sci."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"115","DOI":"10.1016\/j.ins.2017.11.047","article-title":"Structure connectivity and substructure connectivity of k-ary n-cube networks","volume":"433\u2013434","author":"Lv","year":"2018","journal-title":"Inf. Sci."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"2659","DOI":"10.1007\/s40840-019-00827-4","article-title":"Structure and substructure connectivity of balanced hypercubes","volume":"43","author":"Lv","year":"2020","journal-title":"Bull. Malaysian Math. Sci. Soc."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"169","DOI":"10.1016\/j.tcs.2019.09.007","article-title":"Structure connectivity and substructure connectivity of twisted hypercubes","volume":"796","author":"Li","year":"2019","journal-title":"Theor. Comput. Sci."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"C44","DOI":"10.1016\/j.tcs.2017.10.032","article-title":"Structure fault tolerance of hypercubes and folded hypercubes","volume":"711","author":"Sabir","year":"2018","journal-title":"Theor. Comput. Sci."},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"You, L., Han, Y., Wang, X., Zhou, C., Gu, R., and Lu, C. (2018, January 14\u201316). Structure connectivity and substructure connectivity of alternating group graphs. Proceedings of the 2018 IEEE International Conference on Progress in Informatics and Computing (PIC), Suzhou, China.","DOI":"10.1109\/PIC.2018.8706296"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"125639","DOI":"10.1016\/j.amc.2020.125639","article-title":"Structure and substructure connectivity of alternating group graphs","volume":"391","author":"Li","year":"2021","journal-title":"Appl. Math. Comput."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"124632","DOI":"10.1016\/j.amc.2019.124632","article-title":"Structure connectivity and substructure connectivity of bubble-sort star graph networks","volume":"363","author":"Zhang","year":"2019","journal-title":"Appl. Math. Comput."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"8","DOI":"10.1016\/j.tcs.2019.01.036","article-title":"Path and cycle fault tolerance of bubble-sort graph networks","volume":"779","author":"Zhang","year":"2019","journal-title":"Theor. Comput. Sci."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"20","DOI":"10.1016\/j.tcs.2020.10.028","article-title":"Structure connectivity and substructure connectivity of wheel networks","volume":"850","author":"Feng","year":"2021","journal-title":"Theor. Comput. Sci."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"555","DOI":"10.1109\/12.21148","article-title":"A group-theoretic model for symmetric interconnection networks","volume":"38","author":"Akers","year":"1989","journal-title":"IEEE Trans. Comput."},{"key":"ref_18","unstructured":"Chou, Z., Hsu, C., and Sheu, J. (1996, January 3\u20136). Bubble-sort star graphs: A new interconnection network. Proceedings of the International Conference on Parallel and Distributed Systems, Tokyo, Japan."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"715","DOI":"10.1093\/comjnl\/bxy077","article-title":"The strong connectivity of bubble-sort star graphs","volume":"62","author":"Wang","year":"2018","journal-title":"Comput. J."}],"container-title":["Information"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2078-2489\/14\/2\/120\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T18:34:02Z","timestamp":1760121242000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2078-2489\/14\/2\/120"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,2,13]]},"references-count":19,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2023,2]]}},"alternative-id":["info14020120"],"URL":"https:\/\/doi.org\/10.3390\/info14020120","relation":{},"ISSN":["2078-2489"],"issn-type":[{"type":"electronic","value":"2078-2489"}],"subject":[],"published":{"date-parts":[[2023,2,13]]}}}