Reliability analysis of complete cubic networks based on extra conditional fault

Reliability analysis of complete cubic networks based on extra conditional fault | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Reliability analysis of complete cubic networks based on extra conditional fault Mengjie Lv, Xuanli Liu, Hui Dong, Weibei Fan This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-4162729/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 19 Jun, 2024 Read the published version in The Journal of Supercomputing → Version 1 posted 16 You are reading this latest preprint version Abstract The reliability of multiprocessor systems is now a crucial concern in parallel computing. In fact, thanks to rapid and consistent technological advances in networking hardware and software, multiprocessor (core) systems have been successfully implemented. Consequently, there is a notable importance in examining the structures of interprocess communication, with a particular focus on investigating the fault tolerance and fault diagnosability of these structures to build a functionally efficient system. This paper investigates the $s$-extra connectivity ($s$-EC) and $s$-extra diagnosability ($s$-ED) of the complete cubic network $CCN(n)$. Specifically, we initially demonstrate that the $s$-EC of $CCN(n)$ is $\kappa_s(CCN(n))=(s+1)(n+1)-\frac{s(s+3)}{2}$ for $n\geq 3$ and $0\leq s\leq n-2$. Subsequently, we demonstrate that the $s$-ED under the PMC model is $t_s(CCN(n))=(s+1)(n+1)-\frac{s(s+3)}{2}+s$ for $n\geq 3$ and $1\leq s\leq n-2$. Similarly, under the MM* model, the $s$-ED is $t_s(CCN(n))=(s+1)(n+1)-\frac{s(s+3)}{2}+s$ for $n\geq 6$ and $1\leq s\leq \frac{n-2}{4}$. Finally, we conduct simulation experiments, and the results indicate that the $s$-EC consistently surpasses other known connectivities, including classical connectivity and $s$-component connectivity. Additionally, the $s$-ED consistently outperforms classical diagnosability and $s$-component diagnosability of $CCN(n)$. Reliability complete cubic networks extra connectivity extra diagnosability Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Published Journal Publication published 19 Jun, 2024 Read the published version in The Journal of Supercomputing → Version 1 posted Editorial decision: Revision requested 21 Apr, 2024 Reviews received at journal 17 Apr, 2024 Reviews received at journal 16 Apr, 2024 Reviews received at journal 15 Apr, 2024 Reviews received at journal 14 Apr, 2024 Reviews received at journal 07 Apr, 2024 Reviewers agreed at journal 28 Mar, 2024 Reviewers agreed at journal 28 Mar, 2024 Reviewers agreed at journal 28 Mar, 2024 Reviewers agreed at journal 28 Mar, 2024 Reviewers agreed at journal 26 Mar, 2024 Reviewers agreed at journal 26 Mar, 2024 Reviewers invited by journal 26 Mar, 2024 Editor assigned by journal 26 Mar, 2024 Submission checks completed at journal 26 Mar, 2024 First submitted to journal 25 Mar, 2024 You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-4162729","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":284590380,"identity":"1d7a4730-c1fc-4ed4-85e6-4412307e2402","order_by":0,"name":"Mengjie Lv","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAwklEQVRIiWNgGAWjYFCCww0MHxjYIGwe4rQcbGCcAdLCRrwWxgZmsEqiteg2HmyTtt3Bl7hdvoHxwds2BnlzQlrMDgC15J5hS9zZxsBsOLeNwXBnA2Etzca5bWyJG44xsEnztjEkGBwgRoslRAv7b2K1ND5mhNrCTLSWh71tbMY72xKbJeeckzDcQFDLjcMHDvxsOya7nfnwwQ9vymzkCdrCIAFWcYzBABhBIC4h9UDAD1LIUAPUMgpGwSgYBaMABwAAGI5D1HMkEEwAAAAASUVORK5CYII=","orcid":"","institution":"Nanjing University of Posts and Telecommunications","correspondingAuthor":true,"prefix":"","firstName":"Mengjie","middleName":"","lastName":"Lv","suffix":""},{"id":284590381,"identity":"566b62ad-79e9-46f2-a0d2-b1cfe07b6e97","order_by":1,"name":"Xuanli Liu","email":"","orcid":"","institution":"Nanjing University of Posts and Telecommunications","correspondingAuthor":false,"prefix":"","firstName":"Xuanli","middleName":"","lastName":"Liu","suffix":""},{"id":284590382,"identity":"4684450d-0da3-4f4a-9e46-badcf6f731b4","order_by":2,"name":"Hui Dong","email":"","orcid":"","institution":"Nanjing University of Posts and Telecommunications","correspondingAuthor":false,"prefix":"","firstName":"Hui","middleName":"","lastName":"Dong","suffix":""},{"id":284590383,"identity":"c9ff29f4-e053-487b-81e1-2683de33a682","order_by":3,"name":"Weibei Fan","email":"","orcid":"","institution":"Nanjing University of Posts and Telecommunications","correspondingAuthor":false,"prefix":"","firstName":"Weibei","middleName":"","lastName":"Fan","suffix":""}],"badges":[],"createdAt":"2024-03-25 11:02:20","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-4162729/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-4162729/v1","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1007/s11227-024-06272-w","type":"published","date":"2024-06-19T15:46:22+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":58823621,"identity":"bfc849d5-2183-4682-b15a-e2e34fa189e1","added_by":"auto","created_at":"2024-06-21 17:04:12","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":354051,"visible":true,"origin":"","legend":"","description":"","filename":"Reliabilityanalysisofcompletecubicnetworksbasedonextraconditionalfault.pdf","url":"https://assets-eu.researchsquare.com/files/rs-4162729/v1_covered_53b612bd-661d-447d-a4dd-12e48a5f0954.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Reliability analysis of complete cubic networks based on extra conditional fault","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":true,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":true,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"the-journal-of-supercomputing","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"","sideBox":"Learn more about [The Journal of Supercomputing](https://www.springer.com/journal/11227)","snPcode":"11227","submissionUrl":"https://submission.nature.com/new-submission/11227/3","title":"The Journal of Supercomputing","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"Reliability, complete cubic networks, extra connectivity, extra diagnosability","lastPublishedDoi":"10.21203/rs.3.rs-4162729/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-4162729/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"The reliability of multiprocessor systems is now a crucial concern in parallel computing. In fact, thanks to rapid and consistent technological advances in networking hardware and software, multiprocessor (core) systems have been successfully implemented. Consequently, there is a notable importance in examining the structures of interprocess communication, with a particular focus on investigating the fault tolerance and fault diagnosability of these structures to build a functionally efficient system. This paper investigates the $s$-extra connectivity ($s$-EC) and $s$-extra diagnosability ($s$-ED) of the complete cubic network $CCN(n)$. Specifically, we initially demonstrate that the $s$-EC of $CCN(n)$ is $\\kappa_s(CCN(n))=(s+1)(n+1)-\\frac{s(s+3)}{2}$ for $n\\geq 3$ and $0\\leq s\\leq n-2$. Subsequently, we demonstrate that the $s$-ED under the PMC model is $t_s(CCN(n))=(s+1)(n+1)-\\frac{s(s+3)}{2}+s$ for $n\\geq 3$ and $1\\leq s\\leq n-2$. Similarly, under the MM* model, the $s$-ED is $t_s(CCN(n))=(s+1)(n+1)-\\frac{s(s+3)}{2}+s$ for $n\\geq 6$ and $1\\leq s\\leq \\frac{n-2}{4}$. Finally, we conduct simulation experiments, and the results indicate that the $s$-EC consistently surpasses other known connectivities, including classical connectivity and $s$-component connectivity. 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