{"created":"2023-06-20T14:24:13.398676+00:00","id":4870,"links":{},"metadata":{"_buckets":{"deposit":"39515995-e633-4087-b1bc-bb55388322cb"},"_deposit":{"created_by":3,"id":"4870","owners":[3],"pid":{"revision_id":0,"type":"depid","value":"4870"},"status":"published"},"_oai":{"id":"oai:aue.repo.nii.ac.jp:00004870","sets":["724:726"]},"author_link":["30"],"item_4_biblio_info_7":{"attribute_name":"書誌事項","attribute_value_mlt":[{"bibliographicIssueDates":{"bibliographicIssueDate":"2015-11","bibliographicIssueDateType":"Issued"},"bibliographicIssueNumber":"6","bibliographicPageEnd":"1984","bibliographicPageStart":"1973","bibliographicVolumeNumber":"31","bibliographic_titles":[{"bibliographic_title":"Graphs and combinatorics"}]}]},"item_4_description_27":{"attribute_name":"資源タイプ","attribute_value_mlt":[{"subitem_description":"text","subitem_description_type":"Other"}]},"item_4_description_5":{"attribute_name":"抄録","attribute_value_mlt":[{"subitem_description":"Delsarte, Goethals, and Seidel (1977) used the linear programming method in order to find bounds for the size of spherical codes endowed with prescribed inner products between distinct points in the code. In this paper, we develop the linear programming method to obtain bounds for the number of vertices of connected regular graphs endowed with given distinct eigenvalues. This method is proved by some \"dual\" technique of the spherical case, motivated from the theory of association scheme. As an application of this bound, we prove that a connected k-regular graph satisfying g > 2d − 1 has the minimum second-largest eigenvalue of all k-regular graphs of the same size, where d is the number of distinct non-trivial eigenvalues, and g is the girth. The known graphs satisfying g > 2d − 1 are Moore graphs, incidence graphs of regular generalized polygons of order (s, s), triangle-free strongly regular graphs, and the odd graph of degree 4.","subitem_description_type":"Abstract"}]},"item_4_link_3":{"attribute_name":"研究者総覧へのリンク","attribute_value_mlt":[{"subitem_link_text":"Nozaki, Hiroshi","subitem_link_url":"https://souran.aichi-edu.ac.jp/teachers/0c22fe803199abfd.html"}]},"item_4_publisher_8":{"attribute_name":"出版者","attribute_value_mlt":[{"subitem_publisher":"Springer"}]},"item_4_relation_16":{"attribute_name":"関係URI","attribute_value_mlt":[{"subitem_relation_name":[{"subitem_relation_name_text":"http://dx.doi.org/10.1007/s00373-015-1613-7"}],"subitem_relation_type_id":{"subitem_relation_type_id_text":"http://dx.doi.org/10.1007/s00373-015-1613-7","subitem_relation_type_select":"DOI"}}]},"item_4_relation_18":{"attribute_name":"DOI","attribute_value_mlt":[{"subitem_relation_type":"isVersionOf","subitem_relation_type_id":{"subitem_relation_type_id_text":"info:doi/10.1007/s00373-015-1613-7","subitem_relation_type_select":"DOI"}}]},"item_4_rights_12":{"attribute_name":"権利","attribute_value_mlt":[{"subitem_rights":"Copyright: Springer Japan 2015"},{"subitem_rights":"The final publication is available at Springer via http://dx.doi.org/10.1007/s00373-015-1613-7."}]},"item_4_source_id_11":{"attribute_name":"書誌レコードID","attribute_value_mlt":[{"subitem_source_identifier":"AA10451395","subitem_source_identifier_type":"NCID"}]},"item_4_source_id_9":{"attribute_name":"ISSN","attribute_value_mlt":[{"subitem_source_identifier":"0911-0119","subitem_source_identifier_type":"ISSN"}]},"item_4_text_10":{"attribute_name":"書誌情報","attribute_value_mlt":[{"subitem_text_value":"Graphs and combinatorics. 2015, 31(6), p. 1973-1984."}]},"item_4_text_26":{"attribute_name":"著者別名","attribute_value_mlt":[{"subitem_text_value":"ノザキ, ヒロシ"}]},"item_4_text_4":{"attribute_name":"著者(別言語)","attribute_value_mlt":[{"subitem_text_value":"野崎, 寛"}]},"item_4_version_type_14":{"attribute_name":"著者版フラグ","attribute_value_mlt":[{"subitem_version_resource":"http://purl.org/coar/version/c_ab4af688f83e57aa","subitem_version_type":"AM"}]},"item_creator":{"attribute_name":"著者","attribute_type":"creator","attribute_value_mlt":[{"creatorNames":[{"creatorName":"Nozaki, Hiroshi"}],"nameIdentifiers":[{"nameIdentifier":"30","nameIdentifierScheme":"WEKO"},{"nameIdentifier":"80632778","nameIdentifierScheme":"e-Rad","nameIdentifierURI":"https://kaken.nii.ac.jp/ja/search/?qm=80632778"},{"nameIdentifier":"80632778","nameIdentifierScheme":"KAKEN - 研究者検索","nameIdentifierURI":"https://nrid.nii.ac.jp/ja/nrid/1000080632778/"}]}]},"item_files":{"attribute_name":"ファイル情報","attribute_type":"file","attribute_value_mlt":[{"accessrole":"open_date","date":[{"dateType":"Available","dateValue":"2017-03-28"}],"displaytype":"detail","filename":"nozakih001.pdf","filesize":[{"value":"109.5 kB"}],"format":"application/pdf","licensetype":"license_note","mimetype":"application/pdf","url":{"label":"nozakih001.pdf","url":"https://aue.repo.nii.ac.jp/record/4870/files/nozakih001.pdf"},"version_id":"f60e52b6-0dbf-4ea2-bd9b-dbebb525852b"}]},"item_keyword":{"attribute_name":"キーワード","attribute_value_mlt":[{"subitem_subject":"linear programming bound","subitem_subject_scheme":"Other"},{"subitem_subject":"graph spectrum","subitem_subject_scheme":"Other"},{"subitem_subject":"expander graph","subitem_subject_scheme":"Other"},{"subitem_subject":"Ramanujan graph","subitem_subject_scheme":"Other"},{"subitem_subject":"distance-regular graph","subitem_subject_scheme":"Other"},{"subitem_subject":"Moore graph","subitem_subject_scheme":"Other"}]},"item_language":{"attribute_name":"言語","attribute_value_mlt":[{"subitem_language":"eng"}]},"item_resource_type":{"attribute_name":"資源タイプ","attribute_value_mlt":[{"resourcetype":"journal article","resourceuri":"http://purl.org/coar/resource_type/c_6501"}]},"item_title":"Linear programming bounds for regular graphs","item_titles":{"attribute_name":"タイトル","attribute_value_mlt":[{"subitem_title":"Linear programming bounds for regular graphs","subitem_title_language":"en"}]},"item_type_id":"4","owner":"3","path":["726"],"pubdate":{"attribute_name":"公開日","attribute_value":"2016-12-01"},"publish_date":"2016-12-01","publish_status":"0","recid":"4870","relation_version_is_last":true,"title":["Linear programming bounds for regular graphs"],"weko_creator_id":"3","weko_shared_id":3},"updated":"2023-06-20T15:57:00.131905+00:00"}