{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,7]],"date-time":"2026-02-07T19:15:54Z","timestamp":1770491754332,"version":"3.49.0"},"reference-count":26,"publisher":"Oxford University Press (OUP)","issue":"8","license":[{"start":{"date-parts":[[2022,4,26]],"date-time":"2022-04-26T00:00:00Z","timestamp":1650931200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/academic.oup.com\/journals\/pages\/open_access\/funder_policies\/chorus\/standard_publication_model"}],"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":[],"published-print":{"date-parts":[[2023,8,14]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>The diagnosability of a multiprocessor system is of great significance in measuring the reliability and faulty tolerance of interconnection networks. In this paper, we firstly study the diagnosability of a class of Cayley graphs $Cay(H_n,S_n)$ under the PMC model. We prove that $Cay(H_n,S_n)-F$ keeps the strong local diagnosability property even if it has the set $F$ of $(m-2)$ faulty edges and $m-2$ is maximum number of faulty edges, where $m$ is the regular degree of $Cay(H_n,S_n)$. Secondly, we study the diagnosability of $Cay(H_n,S_n)$ with conditional faulty edges under the PMC model. We prove that $Cay(H_n,S_n)-F$ keeps strong local diagnosability property even if it has the set $F$ of $(3m-10)$ faulty edges, provided that each vertex of $Cay(H_n,S_n)-F$ is incident with at least two fault-free edges, where $3m-10$ is maximum number of faulty edges. Finally, we prove that $Cay(H_n,S_n)-F$ keeps strong local diagnosability property no matter how many edges are faulty, provided that each vertex of $Cay(H_n,S_n)-F$ is incident with at least four fault-free edges.<\/jats:p>","DOI":"10.1093\/comjnl\/bxac051","type":"journal-article","created":{"date-parts":[[2022,4,14]],"date-time":"2022-04-14T11:13:14Z","timestamp":1649934794000},"page":"1913-1921","source":"Crossref","is-referenced-by-count":8,"title":["The Local Diagnosability of a Class of Cayley Graphs with Conditional Faulty Edges Under the PMC Model"],"prefix":"10.1093","volume":"66","author":[{"given":"Yunxia","family":"Ren","sequence":"first","affiliation":[{"name":"College of Mathematics and Information Science , Henan Normal University, Xinxiang, Henan 453007, PR China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Shiying","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Mathematics and Computer Science , Shanxi Normal University, Linfen, Shanxi 041004, PR China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"286","published-online":{"date-parts":[[2022,4,26]]},"reference":[{"key":"2023081805144281900_ref1","doi-asserted-by":"crossref","first-page":"47","DOI":"10.1109\/MC.1980.1653532","article-title":"System-level fault diagnosis","volume":"13","author":"Friedman","year":"1980","journal-title":"Computer"},{"key":"2023081805144281900_ref2","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. 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