Classification of n × (n − 1) Incidence Matrices of Gracefully Labeled Simple Graphs

Classification of n × (n − 1) Incidence Matrices of Gracefully Labeled Simple Graphs | 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 Classification of n × (n − 1) Incidence Matrices of Gracefully Labeled Simple Graphs Keneth Adrian Dagal, Kristoffer Karan Hugo This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-3837190/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract This paper presents the distribution of simple graphs with $n$ vertices and $n-1$ edges that admit graceful labeling. This is achieved through a classification table, which considers the graph's diameter (or longest cycle) and the number of isolated vertices. We determine the degree sequences by utilizing the incidence matrices of the labeled graphs mentioned above and subsequently arrange the collection on this classification table. Using the table, we investigate the impact of degree sequences on the diameter (or the longest cycle) value and the existence of isolated vertices. Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Posted Version 1 posted 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. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. 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-3837190","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":266045312,"identity":"74d9afb1-1432-435c-8e5f-ee412a3b82ca","order_by":0,"name":"Keneth Adrian Dagal","email":"data:image/png;base64,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","orcid":"","institution":"Bahrain Polytechnic","correspondingAuthor":true,"prefix":"","firstName":"Keneth","middleName":"Adrian","lastName":"Dagal","suffix":""},{"id":266045313,"identity":"a77c8705-20fb-46f8-9db5-3bc7bf5b4e97","order_by":1,"name":"Kristoffer Karan Hugo","email":"","orcid":"","institution":"National University Laguna","correspondingAuthor":false,"prefix":"","firstName":"Kristoffer","middleName":"Karan","lastName":"Hugo","suffix":""}],"badges":[],"createdAt":"2024-01-05 12:14:13","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-3837190/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-3837190/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":57840545,"identity":"527a0f83-8c23-4025-97d0-018a729ec3cd","added_by":"auto","created_at":"2024-06-06 09:48:46","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":267909,"visible":true,"origin":"","legend":"","description":"","filename":"GTCClassification5.pdf","url":"https://assets-eu.researchsquare.com/files/rs-3837190/v1_covered_f47df023-29d2-4bbb-98f0-94031ba61eee.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"\u003cp\u003eClassification of n × (n − 1) Incidence Matrices of Gracefully Labeled Simple Graphs\u003c/p\u003e","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":true,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"","lastPublishedDoi":"10.21203/rs.3.rs-3837190/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-3837190/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"This paper presents the distribution of simple graphs with $n$ vertices and $n-1$ edges that admit graceful labeling. 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