{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,14]],"date-time":"2026-06-14T22:13:36Z","timestamp":1781475216391,"version":"3.54.1"},"reference-count":44,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2022,11,10]],"date-time":"2022-11-10T00:00:00Z","timestamp":1668038400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100012226","name":"Fundamental Research Funds for the Central Universities","doi-asserted-by":"publisher","award":["BLX201923"],"award-info":[{"award-number":["BLX201923"]}],"id":[{"id":"10.13039\/501100012226","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>Diagnosability plays an important role in appraising the reliability and fault tolerance of symmetrical multiprocessor systems. The novel g-good-neighbor conditional diagnosability restrains that every fault-free node contains at least g fault-free neighbors and is suitable for large scale multiprocessor systems, attracting a lot of research attention. The relationships between the g-good-neighbor connectivity and g-good-neighbor diagnosability of graphs under the MM* model are separately studied, but only applicable in regular graphs or just ranges rather than exact values. As a promising network structure, in 2019, Guo et al. obtained that the g-good-neighbor diagnosability of the exchanged crossed cube (ECQ(s,t)) under the PMC model is 2g(s+2\u2212g)\u22121 (t\u2265s&gt;g). We noticed that the exact value of the g-good-neighbor diagnosability of ECQ(s,t) under the MM* model is still to be determined. In this paper, by proving the upper and lower bounds of the g-good-neighbor diagnosability of ECQ(s,t), for the first time, we derive that the exact value of its g-good-neighbor diagnosability under the MM* model is tgm(ECQ(s,t))=2g(s+2\u2212g)\u22121 (t\u2265s&gt;g), achieving the unity of the g-good-neighbor diagnosability of ECQ(s, t) under both the PMC model and MM* model. Towards the end, simulation experiments are conducted to evaluate the correctness and effectiveness of our conclusion. Our research provides an important supplement to the g-good-neighbor diagnosability of ECQ(s,t).<\/jats:p>","DOI":"10.3390\/sym14112376","type":"journal-article","created":{"date-parts":[[2022,11,10]],"date-time":"2022-11-10T19:18:29Z","timestamp":1668107909000},"page":"2376","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":15,"title":["The g-Good-Neighbor Conditional Diagnosability of Exchanged Crossed Cube under the MM* Model"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-3919-9291","authenticated-orcid":false,"given":"Xinyang","family":"Wang","sequence":"first","affiliation":[{"name":"School of Information Science and Technology, Beijing Forestry University, Beijing 100083, China"},{"name":"Engineering Research Center for Forestry-Oriented Intelligent Information Processing of National Forestry and Grassland Administration, Beijing 100083, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Haozhe","family":"Li","sequence":"additional","affiliation":[{"name":"School of Information Science and Technology, Beijing Forestry University, Beijing 100083, China"},{"name":"Engineering Research Center for Forestry-Oriented Intelligent Information Processing of National Forestry and Grassland Administration, Beijing 100083, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Qiao","family":"Sun","sequence":"additional","affiliation":[{"name":"School of Information Science and Technology, Beijing Forestry University, Beijing 100083, China"},{"name":"Engineering Research Center for Forestry-Oriented Intelligent Information Processing of National Forestry and Grassland Administration, Beijing 100083, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Chen","family":"Guo","sequence":"additional","affiliation":[{"name":"School of Electronic and Information Engineering, Jinggangshan University, Ji\u2019an 343009, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Hu","family":"Zhao","sequence":"additional","affiliation":[{"name":"School of Information Science and Technology, Beijing Forestry University, Beijing 100083, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Xinyu","family":"Wu","sequence":"additional","affiliation":[{"name":"School of Information Science and Technology, Beijing Forestry University, Beijing 100083, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Anqi","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Information Science and Technology, Beijing Forestry University, Beijing 100083, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2022,11,10]]},"reference":[{"key":"ref_1","unstructured":"(2022, August 20). TOP500. ORNL\u2019s Frontier First to Break the Exaflop Ceiling. Available online: https:\/\/www.top500.org\/lists\/top500\/2022\/06\/."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"848","DOI":"10.1109\/PGEC.1967.264748","article-title":"On the connection assignment problem of diagnosable systems","volume":"EC-16","author":"Preparata","year":"1967","journal-title":"IEEE Trans. Electron. Comput."},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Malek, M. (1980, January 6\u20138). A comparison connection assignment for diagnosis of multiprocessor systems. Proceedings of the 7th Annual Symposium on Computer Architecture, La Baule, France.","DOI":"10.1145\/800053.801906"},{"key":"ref_4","unstructured":"Maeng, J., and Malek, M. (1981, January 24\u201326). A comparison connection assignment for self-diagnosis of multiprocesso rsystems. Proceedings of the 11th International Symposium on Fault-Tolerant Computing, Portland, OR, USA."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"1386","DOI":"10.1109\/12.177309","article-title":"On self-diagnosable multiprocessor systems: Diagnosis by the comparison approach","volume":"41","author":"Sengupta","year":"1992","journal-title":"IEEE Trans. Comput."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"69","DOI":"10.1080\/17445760.2019.1600688","article-title":"Diagnosability of arrangement graphs with missing edges under the MM* model","volume":"35","author":"Wang","year":"2020","journal-title":"Int. J. Parallel Emergent Distrib. Syst."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.tcs.2018.07.019","article-title":"Hybrid fault diagnosis capability analysis of hypercubes under the PMC model and MM* model","volume":"758","author":"Zhu","year":"2019","journal-title":"Theor. Comput. Sci."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"81","DOI":"10.1016\/j.tcs.2018.06.046","article-title":"The g-good-neighbor conditional diagnosability of the crossed cubes under the PMC and MM* model","volume":"755","author":"Guo","year":"2019","journal-title":"Theor. Comput. Sci."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"42","DOI":"10.4236\/ajcm.2018.81004","article-title":"The 2-extra diagnosability of alternating group graphs under the PMC model and MM* model","volume":"8","author":"Wang","year":"2018","journal-title":"Am. J. Comput. Math."},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Wang, S., and Ren, Y. (2018). g-Good-neighbor diagnosability of arrangement graphs under the PMC model and MM* model. Information, 9.","DOI":"10.3390\/info9110275"},{"key":"ref_11","first-page":"484","article-title":"The g-good neighbor conditional diagnosability of twisted hypercubes under the PMC and MM* model","volume":"332","author":"Liu","year":"2018","journal-title":"Appl. Math. Comput."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"61151","DOI":"10.1109\/ACCESS.2018.2875785","article-title":"Conditional Diagnosability of Exchanged Hypercube Under the MM* Model","volume":"6","author":"Guo","year":"2018","journal-title":"IEEE Access"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"1221","DOI":"10.1007\/s11464-017-0657-9","article-title":"g-Good-neighbor conditional diagnosability of star graph networks under PMC model and MM* model","volume":"12","author":"Wang","year":"2017","journal-title":"Front. Math. China"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"574","DOI":"10.1016\/j.ipl.2016.04.005","article-title":"The g-good-neighbor conditional diagnosability of n-dimensional hypercubes under the MM\u204e model","volume":"116","author":"Wang","year":"2016","journal-title":"Inf. Process. Lett."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"30","DOI":"10.1016\/j.tcs.2021.10.015","article-title":"The Rg-conditional diagnosability of international networks","volume":"898","author":"Yuan","year":"2022","journal-title":"Theor. Comput. Sci."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"310","DOI":"10.1016\/j.dam.2021.04.004","article-title":"The 3-extra conditional diagnosability of balanced hypercubes under MM\u2217 model","volume":"309","author":"Li","year":"2022","journal-title":"Discret. Appl. Math."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"165","DOI":"10.1109\/TC.2005.19","article-title":"Conditional diagnosability measures for large multiprocessor systems","volume":"54","author":"Lai","year":"2005","journal-title":"IEEE Trans. Comput."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"140","DOI":"10.1016\/j.sysarc.2008.10.005","article-title":"Conditional diagnosability of hypercubes under the comparison diagnosis model","volume":"55","author":"Hsu","year":"2009","journal-title":"J. Syst. Archit."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"207","DOI":"10.1109\/TDSC.2016.2562620","article-title":"Conditional Diagnosability of (n, k)-Star Graphs Under the PMC Model","volume":"15","author":"Chang","year":"2016","journal-title":"IEEE Trans. Dependable Secur. Comput."},{"key":"ref_20","first-page":"106","article-title":"Conditional diagnosability of exchanged crossed cube under the MM model","volume":"38","author":"Guo","year":"2017","journal-title":"J. Commun."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"1069","DOI":"10.1016\/j.ins.2007.09.005","article-title":"On conditional diagnosability of the folded hypercubes","volume":"178","author":"Zhu","year":"2008","journal-title":"Inf. Sci."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"43","DOI":"10.1016\/j.tcs.2017.02.010","article-title":"Conditional diagnosability of a class of matching composition networks under the comparison model","volume":"674","author":"Xu","year":"2017","journal-title":"Theor. Comput. Sci."},{"key":"ref_23","first-page":"1","article-title":"Conditional diagnosability of Cayley graphs generated by transposition trees under the PMC model","volume":"20","author":"Chang","year":"2015","journal-title":"ACM Trans. Des. Autom. Electron. Syst. (TODAES)"},{"key":"ref_24","first-page":"10406","article-title":"The g-good-neighbor conditional diagnosability of hypercube under PMC model","volume":"218","author":"Peng","year":"2012","journal-title":"Appl. Math. Comput."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"1165","DOI":"10.1109\/TPDS.2014.2318305","article-title":"The g-Good-Neighbor Conditional Diagnosability of k-Ary n-Cubes under the PMC Model and MM* Model","volume":"26","author":"Yuan","year":"2014","journal-title":"IEEE Trans. Parallel Distrib. Syst."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"333","DOI":"10.1007\/s40305-017-0166-2","article-title":"The g-good-neighbor conditional diagnosability of locally twisted cubes","volume":"6","author":"Wei","year":"2018","journal-title":"J. Oper. Res. Soc. China"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"91","DOI":"10.1016\/j.tcs.2017.07.030","article-title":"The g-good-neighbor diagnosability of locally twisted cubes","volume":"697","author":"Ren","year":"2017","journal-title":"Theor. Comput. Sci."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"1741001","DOI":"10.1142\/S0219265917410018","article-title":"The 1-Good-Neighbor Conditional Diagnosability of Some Regular Graphs","volume":"17","author":"Gu","year":"2017","journal-title":"J. Interconnect. Netw."},{"key":"ref_29","first-page":"295","article-title":"The 1,2-good-neighbor conditional diagnosabilities of regular graphs","volume":"334","author":"Wei","year":"2018","journal-title":"Appl. Math. Comput."},{"key":"ref_30","first-page":"241","article-title":"The 2-good-neighbor (2-extra) diagnosability of alternating group graph networks under the PMC model and MM* model","volume":"305","author":"Wang","year":"2017","journal-title":"Appl. Math. Comput."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"285","DOI":"10.1109\/TR.2017.2760905","article-title":"The Relationship Between g-Restricted Connectivity and g-Good-Neighbor Fault Diagnosability of General Regular Networks","volume":"67","author":"Lin","year":"2018","journal-title":"IEEE Trans. Reliab."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"47","DOI":"10.1080\/23799927.2018.1441187","article-title":"A relationship between g-good-neighbour conditional diagnosability and g-good-neighbour connectivity in regular graphs","volume":"3","author":"Cheng","year":"2018","journal-title":"Int. J. Comput. Math. Comput. Syst. Theory"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"56","DOI":"10.1016\/j.tcs.2018.07.018","article-title":"A general approach to deriving the g-good-neighbor conditional diagnosability of interconnection networks","volume":"757","author":"Cheng","year":"2019","journal-title":"Theor. Comput. Sci."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"107","DOI":"10.1016\/j.tcs.2018.09.002","article-title":"The g-good-neighbor and g-extra diagnosability of networks","volume":"773","author":"Wang","year":"2019","journal-title":"Theor. Comput. Sci."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"2211","DOI":"10.1109\/TPDS.2012.330","article-title":"Exchanged crossed cube: A novel interconnection network for parallel computation","volume":"24","author":"Li","year":"2012","journal-title":"IEEE Trans. Parallel Distrib. Syst."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"866","DOI":"10.1109\/TPDS.2005.113","article-title":"The exchanged hypercube","volume":"16","author":"Loh","year":"2005","journal-title":"IEEE Trans. Parallel Distrib. Syst."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"513","DOI":"10.1109\/71.159036","article-title":"The crossed cube architecture for parallel computation","volume":"3","author":"Efe","year":"1992","journal-title":"IEEE Trans. Parallel Distrib. Syst."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"80","DOI":"10.1016\/j.ipl.2015.10.003","article-title":"The super connectivity of exchanged crossed cube","volume":"116","author":"Ning","year":"2016","journal-title":"Inf. Process. Lett."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"65","DOI":"10.1016\/j.tcs.2017.07.023","article-title":"The h-connectivity of exchanged crossed cube","volume":"696","author":"Ning","year":"2017","journal-title":"Theor. Comput. Sci."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"394","DOI":"10.1016\/j.ipl.2014.10.017","article-title":"The connectivity of exchanged crossed cube","volume":"115","author":"Ning","year":"2015","journal-title":"Inf. Process. Lett."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"29994","DOI":"10.1109\/ACCESS.2018.2844468","article-title":"The conditional diagnosability of exchanged crossed cube","volume":"6","author":"Guo","year":"2018","journal-title":"IEEE Access"},{"key":"ref_42","first-page":"92","article-title":"Research on g-Good-Neighbor Conditional Diagnosability of Exchanged Crossed Cube","volume":"51\u201358","author":"Peng","year":"2019","journal-title":"Comput. Eng. Appl."},{"key":"ref_43","unstructured":"Bondy, J.A., and Murty, U.S.R. (2010). Graph Theory, Springer."},{"key":"ref_44","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."}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/14\/11\/2376\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T01:13:53Z","timestamp":1760145233000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/14\/11\/2376"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,11,10]]},"references-count":44,"journal-issue":{"issue":"11","published-online":{"date-parts":[[2022,11]]}},"alternative-id":["sym14112376"],"URL":"https:\/\/doi.org\/10.3390\/sym14112376","relation":{},"ISSN":["2073-8994"],"issn-type":[{"value":"2073-8994","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,11,10]]}}}