Closeness of Some Tree Structures

Closeness of Some Tree Structures | 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Share Download PDF Research Article Closeness of Some Tree Structures hande tuncel golpek This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-1797186/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 13 Nov, 2023 Read the published version in Soft Computing → Version 1 posted 3 You are reading this latest preprint version Abstract A graph can be analyzed by means of many graph theoretical parameters and formulas derived from them. One of those parameters is the closeness parameter which is modified to enable calculations in disconnected graphs. In thispaper, we have considered closeness of some tree structures as k-ary tree, binomial trees, binary tree, comet, double comet, double star graph and E p t graph. Upper and lower bounds are investigated for k-ary andbinary trees. Upper bounds comes from perfect form of tree for k-ary tree andits special structure binary tree. Therefore, the closeness values of perfect forms have been formulated. Also, closeness formulas are gained for binomial trees, comet, double comet, double star graphs and E p t graph. MSC Classification: 05C05, 05C12, 68R10 Graph vulnerability Closeness Tree Full Text Cite Share Download PDF Status: Published Journal Publication published 13 Nov, 2023 Read the published version in Soft Computing → Version 1 posted Reviewers invited by journal 26 Nov, 2022 Editor assigned by journal 27 Jun, 2022 First submitted to journal 26 Jun, 2022 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-1797186","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":155215640,"identity":"b026d409-ac15-4cca-985d-d7003b6f4a08","order_by":0,"name":"hande tuncel golpek","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA7ElEQVRIiWNgGAWjYBACAyCWgLIZD3xggwsS1AJRdHAGXEsCkVoO8xCjxZz97MEbHxj+JG5nP3zgsE2ZTWIDe/M2CcYf93BqsezJS7acwWCQuLMnLeFwzrm0xAaeY2USDAnFuB12IMdMmgeoZcMNHoPDuW2HExskcsyAWnC7zOD8GzPpP2At/B8OW7b9T2yQf0NAyw2gLQwQWxgOM7YdANrCQ0jLG2PLHgNj4w1n0gwO9pxLNm7jSSu2SEjD57Acwxs/KuRkNxw//PDBjzI72X72wxtvfLDBrQWqEYkNjhpCGkbBKBgFo2AU4AcAP8dUopC+E2UAAAAASUVORK5CYII=","orcid":"https://orcid.org/0000-0001-9183-6732","institution":"Dokuz Eylul University: Dokuz Eylul Universitesi","correspondingAuthor":true,"submittingAuthor":false,"prefix":"","firstName":"hande","middleName":"tuncel","lastName":"golpek","suffix":""}],"badges":[],"createdAt":"2022-06-26 16:39:31","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-1797186/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-1797186/v1","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1007/s00500-023-09395-z","type":"published","date":"2023-11-13T15:01:38+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":46779988,"identity":"9200eb11-5f89-493d-90e9-1a59f911cb69","added_by":"auto","created_at":"2023-11-20 15:08:43","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":332013,"visible":true,"origin":"","legend":"","description":"","filename":"socoHTG.pdf","url":"https://assets-eu.researchsquare.com/files/rs-1797186/v1_covered_8f82e43c-3d11-46eb-8d99-028179ca35f9.pdf"}],"financialInterests":"","formattedTitle":"Closeness of Some Tree Structures","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":true,"isPdf":true,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"soft-computing","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"soco","sideBox":"Learn more about [Soft Computing](https://www.springer.com/journal/500)","snPcode":"500","submissionUrl":"https://submission.nature.com/new-submission/500/3","title":"Soft Computing","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"Graph vulnerability, Closeness, Tree","lastPublishedDoi":"10.21203/rs.3.rs-1797186/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-1797186/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eA graph can be analyzed by means of many graph theoretical parameters and formulas derived from them. 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