REGULARITY AND UNIMODALITY OF $h-$POLYNOMIAL OFCORONA GRAPHS

REGULARITY AND UNIMODALITY OF $h-$POLYNOMIAL OFCORONA 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 REGULARITY AND UNIMODALITY OF $h-$POLYNOMIAL OFCORONA GRAPHS Trong Hoang Do, My Hanh Pham, Nam Trung Tran This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-2849900/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 Let H = { H v : v ∈ V ( G )} be a family of nonempty graphs indexed by the vertex set of a graph G . The corona graph G ◦ H of G and H is the disjoint union of G and H v , v ∈ V ( G ), with additional edges joining each vertex v ∈ V ( G ) to all the vertices of H v . In this paper, we are deeply concerned in investigating the (induced) matching number of the graph G ◦ H . It gives a formula for the Castelnuovo–Mumford regularity of edge ideal of this graph. Additionally, we propose a close relationship between independence polynomial of corona graph G ◦ H and h-polynomial of its independence simplicial complexes. Thereby, the formula of h-polynomial of G◦H is established and some properties of its unimodality and real-rootedness are presented. 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. 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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-2849900","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":194772361,"identity":"53699622-2a7a-4d80-83f8-d06d2fa8a077","order_by":0,"name":"Trong Hoang Do","email":"","orcid":"","institution":"Hanoi University of Science and Technology","correspondingAuthor":false,"submittingAuthor":false,"prefix":"","firstName":"Trong","middleName":"Hoang","lastName":"Do","suffix":""},{"id":194772362,"identity":"ad580c2f-19b0-46b7-8758-77592463cbbb","order_by":1,"name":"My Hanh Pham","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAwUlEQVRIiWNgGAWjYFACHgYGxgYbOJtoLWmkazlMghZzsbMHPxfuOC8vH5HA+OBtG0PidkJaLGfnJUvPPHPbcOONBGbDuUAtOxsIaDG4nWMgzdt2m3HjjAQ2IIPB2OAAYS3Gv3nbztkDtbD/JlaLGdDwA4nzJRLYmIFa5AhqsZydY2bN25acvIHnYbPknHMShLWYS+cY3+Zts7Od35588MObMhsewg6DMw4wNgApCQLqkbXINxBWPApGwSgYBSMUAAATdD4BYqoAtQAAAABJRU5ErkJggg==","orcid":"","institution":"An Giang University","correspondingAuthor":true,"submittingAuthor":false,"prefix":"","firstName":"My","middleName":"Hanh","lastName":"Pham","suffix":""},{"id":194772363,"identity":"6c09e7f0-ba3c-4f1c-b968-610198eb3c1a","order_by":2,"name":"Nam Trung Tran","email":"","orcid":"","institution":"Institute of Mathematics","correspondingAuthor":false,"submittingAuthor":false,"prefix":"","firstName":"Nam","middleName":"Trung","lastName":"Tran","suffix":""}],"badges":[],"createdAt":"2023-04-23 04:29:17","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-2849900/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-2849900/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":36582491,"identity":"1cb19bc9-04f9-4347-9bf9-30745f0a5d06","added_by":"auto","created_at":"2023-05-03 15:14:41","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":330948,"visible":true,"origin":"","legend":"","description":"","filename":"CoronagraphsApril23.pdf","url":"https://assets-eu.researchsquare.com/files/rs-2849900/v1_covered_9042f6ac-53c0-4e70-8e26-a34d8c15b573.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"REGULARITY AND UNIMODALITY OF $h-$POLYNOMIAL OFCORONA GRAPHS","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-2849900/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-2849900/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eLet \u003cem\u003eH = \u003c/em\u003e{\u003cem\u003eH\u003c/em\u003e\u003csub\u003e\u003cem\u003ev\u003c/em\u003e\u003c/sub\u003e\u003cem\u003e : v \u003c/em\u003e∈ \u003cem\u003eV \u003c/em\u003e(\u003cem\u003eG\u003c/em\u003e)} be a family of nonempty graphs indexed by the vertex set of a graph \u003cem\u003eG\u003c/em\u003e. The corona graph \u003cem\u003eG\u003c/em\u003e ◦ \u003cem\u003eH \u003c/em\u003eof \u003cem\u003eG\u003c/em\u003e and \u003cem\u003eH\u003c/em\u003e is the disjoint union of \u003cem\u003eG\u003c/em\u003e and\u003cem\u003e H\u003c/em\u003e\u003csub\u003e\u003cem\u003ev\u003c/em\u003e\u003c/sub\u003e\u003cem\u003e, v \u003c/em\u003e∈\u003cem\u003e V\u003c/em\u003e (\u003cem\u003eG\u003c/em\u003e), with additional edges joining each vertex \u003cem\u003ev\u003c/em\u003e ∈ \u003cem\u003eV\u003c/em\u003e (\u003cem\u003eG\u003c/em\u003e) to all the vertices of \u003cem\u003eH\u003c/em\u003e\u003csub\u003e\u003cem\u003ev\u003c/em\u003e\u003c/sub\u003e. In this paper, we are deeply concerned in investigating the (induced) matching number of the graph \u003cem\u003eG ◦ H\u003c/em\u003e. It gives a formula for the Castelnuovo–Mumford regularity of edge ideal of this graph. Additionally, we propose a close relationship between independence polynomial of corona graph \u003cem\u003eG ◦ H\u003c/em\u003e and h-polynomial of its independence simplicial complexes. Thereby, the formula of h-polynomial of \u003cem\u003eG◦H\u003c/em\u003e is established and some properties of its unimodality and real-rootedness are presented.\u003c/p\u003e","manuscriptTitle":"REGULARITY AND UNIMODALITY OF $h-$POLYNOMIAL OFCORONA GRAPHS","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2023-04-27 10:54:53","doi":"10.21203/rs.3.rs-2849900/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","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}}],"origin":"","ownerIdentity":"71421598-6ed8-4c36-bdcf-b674aa9d0615","owner":[],"postedDate":"April 27th, 2023","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[],"tags":[],"updatedAt":"2023-05-03T15:14:31+00:00","versionOfRecord":[],"versionCreatedAt":"2023-04-27 10:54:53","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-2849900","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-2849900","identity":"rs-2849900","version":["v1"]},"buildId":"7rjqhiLT3MXkJMwkYKINL","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}