{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,6]],"date-time":"2026-03-06T14:39:39Z","timestamp":1772807979420,"version":"3.50.1"},"reference-count":34,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2018,11,7]],"date-time":"2018-11-07T00:00:00Z","timestamp":1541548800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"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"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Information"],"abstract":"<jats:p>Diagnosability of a multiprocessor system is an important research topic. The system and interconnection network has a underlying topology, which usually presented by a graph     G = ( V , E )    . In 2012, a measurement for fault tolerance of the graph was proposed by Peng et al. This measurement is called the g-good-neighbor diagnosability that restrains every fault-free node to contain at least g fault-free neighbors. Under the PMC model, to diagnose the system, two adjacent nodes in G are can perform tests on each other. Under the MM model, to diagnose the system, a node sends the same task to two of its neighbors, and then compares their responses. The MM* is a special case of the MM model and each node must test its any pair of adjacent nodes of the system. As a famous topology structure, the     ( n , k )    -arrangement graph     A  n , k     , has many good properties. In this paper, we give the g-good-neighbor diagnosability of     A  n , k      under the PMC model and MM* model.<\/jats:p>","DOI":"10.3390\/info9110275","type":"journal-article","created":{"date-parts":[[2018,11,7]],"date-time":"2018-11-07T10:32:07Z","timestamp":1541586727000},"page":"275","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["g-Good-Neighbor Diagnosability of Arrangement Graphs under the PMC Model and MM* Model"],"prefix":"10.3390","volume":"9","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-9335-3005","authenticated-orcid":false,"given":"Shiying","family":"Wang","sequence":"first","affiliation":[{"name":"College of Mathematics and Information Science, Henan Normal University, Xinxiang 453007, Henan, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yunxia","family":"Ren","sequence":"additional","affiliation":[{"name":"College of Mathematics and Information Science, Henan Normal University, Xinxiang 453007, Henan, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2018,11,7]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"486","DOI":"10.1109\/TC.1984.1676472","article-title":"An O(n2.5) Fault identification algorithm for diagnosable systems","volume":"33","author":"Dahbura","year":"1984","journal-title":"IEEE Trans. Comput."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"1099","DOI":"10.1109\/TPDS.2002.1041887","article-title":"Diagnosability of crossed cubes under the comparison diagnosis model","volume":"13","author":"Fan","year":"2002","journal-title":"IEEE Trans. Parallel Distrib. Syst."},{"key":"ref_3","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_4","doi-asserted-by":"crossref","first-page":"848","DOI":"10.1109\/PGEC.1967.264748","article-title":"On the connection assignment problem of diagnosable systems","volume":"16","author":"Preparata","year":"1967","journal-title":"IEEE Trans. Comput. EC"},{"key":"ref_5","unstructured":"Maeng, J., and Malek, M. (1981, January 24\u201326). A comparison connection assignment for self-diagnosis of multiprocessor systems. Proceedings of the 11th International Symposium on Fault-Tolerant Computing, Portland, ME, USA."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"10406","DOI":"10.1016\/j.amc.2012.03.092","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_7","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* model","volume":"116","author":"Wang","year":"2016","journal-title":"Inf. Process. Lett."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"108","DOI":"10.2174\/2213275910666161207162427","article-title":"The 1-good-neighbor diagnosability of alternating group graph networks under the PMC model and MM* model","volume":"10","author":"Jirimutu","year":"2017","journal-title":"Recent Patents Comput. Sci."},{"key":"ref_9","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_10","doi-asserted-by":"crossref","first-page":"259","DOI":"10.4236\/ajcm.2016.63027","article-title":"Some properties of the g-good-neighbor (g-extra) diagnosability of a multiprocessor system","volume":"6","author":"Ren","year":"2016","journal-title":"Am. J. Comput. Math."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"620","DOI":"10.1080\/00207160.2015.1119817","article-title":"The 1-good-neighbor diagnosability of Cayley graphs generated by transposition trees under the PMC model and MM* model","volume":"94","author":"Wang","year":"2017","journal-title":"Int. J. Comput. Math."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"92","DOI":"10.1016\/j.tcs.2016.03.019","article-title":"The 2-good-neighbor diagnosability of Cayley graphs generated by transposition trees under the PMC model and MM* model","volume":"628","author":"Wang","year":"2016","journal-title":"Theor. Comput. Sci."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"108","DOI":"10.1016\/j.dam.2017.02.023","article-title":"The 1-good-neighbor connectivity and diagnosability of Cayley graphs generated by complete graphs","volume":"246","author":"Wang","year":"2018","journal-title":"Discr. Appl. Math."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"71","DOI":"10.1051\/ita\/2017008","article-title":"The connectivity and nature diagnosability of expanded k-ary n-cubes","volume":"51","author":"Wang","year":"2017","journal-title":"RAIRO-Theor. Inf. Appl."},{"key":"ref_15","first-page":"55","article-title":"The nature diagnosability of bubble-sort star graph networks under the PMC model and MM* model","volume":"4","author":"Wang","year":"2017","journal-title":"Int. J. Eng. Appl. Sci."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"241","DOI":"10.1016\/j.amc.2017.02.006","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_17","doi-asserted-by":"crossref","first-page":"691","DOI":"10.1016\/j.dam.2016.09.047","article-title":"The 2-good-neighbor connectivity and 2-good-neighbor diagnosability of bubble-sort star graph networks","volume":"217","author":"Wang","year":"2017","journal-title":"Discr. Appl. Math."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"1850005","DOI":"10.1142\/S0219265918500056","article-title":"A note on the nature diagnosability of alternating group graphs under the PMC model and MM* model","volume":"18","author":"Wang","year":"2018","journal-title":"J. Interconnect. Netw."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"1221","DOI":"10.1007\/s11464-017-0657-9","article-title":"The g-good-neighbor conditional diagnosability of star graph networks under the PMC model and MM* model","volume":"12","author":"Wang","year":"2017","journal-title":"Front. Math. China"},{"key":"ref_20","first-page":"70","article-title":"The tightly super 2-good-neighbor connectivity and 2-good-neighbor diagnosability of crossed cubes","volume":"3","author":"Wang","year":"2017","journal-title":"Int. J. New Technol. Res."},{"key":"ref_21","first-page":"66","article-title":"The 1-good-neighbor diagnosability of shuffle-cubes","volume":"3","author":"Wang","year":"2017","journal-title":"Int. J. New Technol. Res."},{"key":"ref_22","first-page":"625","article-title":"Reliability of complete cubic networks under the condition of g-good-neighbor","volume":"60","author":"Xu","year":"2017","journal-title":"Comput. J."},{"key":"ref_23","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":"2015","journal-title":"IEEE Trans. Parallel Distrib. Syst."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"144","DOI":"10.1016\/j.tcs.2016.01.046","article-title":"g-Good-neighbor conditional diagnosability measures for 3-ary n-cube networks","volume":"622","author":"Yuan","year":"2016","journal-title":"Theor. Comput. Sci."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"555","DOI":"10.1109\/12.21148","article-title":"Akers, Balakrishnan Krishnamurthy, A group theoretic model for symmetric interconnection networks","volume":"38","author":"Akers","year":"1989","journal-title":"IEEE Trans. Comput."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"235","DOI":"10.1016\/0020-0190(92)90030-Y","article-title":"Arrangement graphs: A class of generalized star graphs","volume":"42","author":"Day","year":"1992","journal-title":"Inf. Process. Lett."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"281","DOI":"10.1002\/net.21476","article-title":"Linearly many faults in arrangement graphs","volume":"61","author":"Cheng","year":"2013","journal-title":"Networks"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"3669","DOI":"10.1007\/s11227-017-1964-3","article-title":"On the restricted connectivity of the arrangement graph","volume":"73","author":"Cheng","year":"2017","journal-title":"J. Supercomput."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"215","DOI":"10.1016\/S0020-0190(98)00052-0","article-title":"On the arrangement graph","volume":"66","author":"Chiang","year":"1998","journal-title":"Inf. Process. Lett."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"1002","DOI":"10.1109\/12.238494","article-title":"Embedding of cycles in arrangement graphs","volume":"42","author":"Day","year":"1993","journal-title":"IEEE Trans. Comput."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"79","DOI":"10.1016\/j.tcs.2014.06.041","article-title":"Conditional diagnosability of arrangement graphs under the PMC model","volume":"548","author":"Lin","year":"2014","journal-title":"Theor. Comput. Sci."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"1037","DOI":"10.1016\/j.ipl.2011.07.017","article-title":"Conditional fault tolerance of arrangement graphs","volume":"111","author":"Zhou","year":"2011","journal-title":"Inf. Process. Lett."},{"key":"ref_33","doi-asserted-by":"crossref","unstructured":"Bondy, J.A., and Murty, U.S.R. (2007). Graph Theory, Springer.","DOI":"10.1007\/978-3-7643-7400-6"},{"key":"ref_34","unstructured":"Wang, S., and Ma, X. Diagnosability of arrangement graphs with missing edges under MM* model, Appl. Math. Comput., to appear."}],"container-title":["Information"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2078-2489\/9\/11\/275\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T15:28:25Z","timestamp":1760196505000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2078-2489\/9\/11\/275"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,11,7]]},"references-count":34,"journal-issue":{"issue":"11","published-online":{"date-parts":[[2018,11]]}},"alternative-id":["info9110275"],"URL":"https:\/\/doi.org\/10.3390\/info9110275","relation":{},"ISSN":["2078-2489"],"issn-type":[{"value":"2078-2489","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,11,7]]}}}