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The \"augmented graph\" is a graph obtained by addition of some vertices and edges to a given graph which is called \"basic graph\" in this paper. If the vertices in a basic graph are denoted by v_i (i=1, 2, …, m), those added to the basic graph by W_j (j=1, 2, …, n), and the length of the edge between vertices w_j and v_i by d_\u003cji\u003e, the minimax, maximin, maximum, and minimum points are the points w_j\u0027s which have the lengths d_\u003cji\u003e^*, d_\u003cji\u003e^\u003c**\u003e, S^*, and S^\u003c**\u003e defined by d_\u003cjt\u003e^* = \u003cmin\u003e___j \u003cmax\u003e___i d_\u003cjt\u003e d_\u003cji\u003e^\u003c**\u003e = \u003cmax\u003e___j \u003cmin\u003e___i d_\u003cji\u003e S^* = \u003cmax\u003e___j Σ^m__\u003ci=1\u003ed_\u003cji\u003e S^\u003c**\u003e = \u003cmin\u003e___j Σ^m__\u003ci=1\u003ed_\u003cji\u003e respectively. And the dual augmented graph is the graph obtained by regarding the w_j\u0027s (j=1, 2, …, n) as the vertices in a new basic graph and the v_i\u0027s (i=1, 2, …, m) as the vertices added to the new basic graph. The minimax, maximin, maximum, and minimum points are the points v_i\u0027s which have the lengths d_\u003cij\u003e^*, d_\u003cij\u003e^\u003c**\u003e, S^*, and S^\u003c**\u003e denned by d_\u003cij\u003e^* = \u003cmin\u003e___i \u003cmax\u003e___j d_\u003cij\u003e d_\u003cij\u003e^\u003c**\u003e = \u003cmax\u003e___i \u003cmin\u003e___j d_\u003cij\u003e S^* = \u003cmax\u003e___i Σ^n__\u003cj=1\u003e d_\u003cij\u003e S^\u003c**\u003e = \u003cmin\u003e___i Σ^n__\u003cj=1\u003e d_\u003cij\u003e respectively. Incidentally, using augmented and the dual augmented graphs, I tried to examine the positions of the facilities for disposal of garbage in Tokyo.", "subitem_description_type": "Other"}]}, "item_2_full_name_8": {"attribute_name": "著者名(英)", "attribute_value_mlt": [{"nameIdentifiers": [{"nameIdentifier": "8687", "nameIdentifierScheme": "WEKO"}], "names": [{"name": "SUZUKI, KEISUKE", "nameLang": "en"}]}]}, "item_2_source_id_13": {"attribute_name": "雑誌書誌ID", "attribute_value_mlt": [{"subitem_source_identifier": "AN00251278", "subitem_source_identifier_type": "NCID"}]}, "item_2_text_10": {"attribute_name": "著者所属(英)", "attribute_value_mlt": [{"subitem_text_language": "en", "subitem_text_value": "Ryutsu Keizai University"}]}, "item_2_text_2": {"attribute_name": "記事種別(日)", "attribute_value_mlt": [{"subitem_text_value": "論文"}]}, "item_2_text_3": {"attribute_name": "記事種別(英)", "attribute_value_mlt": [{"subitem_text_language": "en", "subitem_text_value": "Article"}]}, "item_2_text_9": {"attribute_name": "著者所属(日)", "attribute_value_mlt": [{"subitem_text_value": "流通経済大学"}]}, "item_files": {"attribute_name": "ファイル情報", "attribute_type": "file", "attribute_value_mlt": [{"accessrole": "open_date", "date": [{"dateType": "Available", "dateValue": "1977-01-01"}], "displaytype": "detail", "download_preview_message": "", "file_order": 0, "filename": "KJ00005535643.pdf", "filesize": [{"value": "1.5 MB"}], "format": "application/pdf", "future_date_message": "", "is_thumbnail": false, "licensetype": "license_free", "mimetype": "application/pdf", "size": 1500000.0, "url": {"url": "https://rku.repo.nii.ac.jp/record/3702/files/KJ00005535643.pdf"}, "version_id": "71cb2ce9-8769-4be7-8c20-662b8bc3b1f8"}]}, "item_language": {"attribute_name": "言語", "attribute_value_mlt": [{"subitem_language": "jpn"}]}, "item_resource_type": {"attribute_name": "資源タイプ", "attribute_value_mlt": [{"resourcetype": "departmental bulletin paper", "resourceuri": "http://purl.org/coar/resource_type/c_6501"}]}, "item_title": "グラフにおけるminimax, maximin, maximum, minimum点 : 廃棄物処理施設の建設地点に関する考察", "item_titles": {"attribute_name": "タイトル", "attribute_value_mlt": [{"subitem_title": "グラフにおけるminimax, maximin, maximum, minimum点 : 廃棄物処理施設の建設地点に関する考察"}, {"subitem_title": "Minimax, maximin, maximum, and minimum points in a graph : An investigation of the positions of facilities of disposal of garbage", "subitem_title_language": "en"}]}, "item_type_id": "2", "owner": "3", "path": ["670"], "permalink_uri": "https://rku.repo.nii.ac.jp/records/3702", "pubdate": {"attribute_name": "公開日", "attribute_value": "1977-01-01"}, "publish_date": "1977-01-01", "publish_status": "0", "recid": "3702", "relation": {}, "relation_version_is_last": true, "title": ["グラフにおけるminimax, maximin, maximum, minimum点 : 廃棄物処理施設の建設地点に関する考察"], "weko_shared_id": -1}
グラフにおけるminimax, maximin, maximum, minimum点 : 廃棄物処理施設の建設地点に関する考察
https://rku.repo.nii.ac.jp/records/3702
https://rku.repo.nii.ac.jp/records/370244c87200-6063-4dbf-9a8e-e95620cde7cf
名前 / ファイル | ライセンス | アクション |
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KJ00005535643.pdf (1.5 MB)
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Item type | 紀要論文(ELS) / Departmental Bulletin Paper(1) | |||||
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公開日 | 1977-01-01 | |||||
タイトル | ||||||
タイトル | グラフにおけるminimax, maximin, maximum, minimum点 : 廃棄物処理施設の建設地点に関する考察 | |||||
タイトル | ||||||
言語 | en | |||||
タイトル | Minimax, maximin, maximum, and minimum points in a graph : An investigation of the positions of facilities of disposal of garbage | |||||
言語 | ||||||
言語 | jpn | |||||
資源タイプ | ||||||
資源タイプ識別子 | http://purl.org/coar/resource_type/c_6501 | |||||
資源タイプ | departmental bulletin paper | |||||
ページ属性 | ||||||
内容記述タイプ | Other | |||||
内容記述 | P(論文) | |||||
記事種別(日) | ||||||
論文 | ||||||
記事種別(英) | ||||||
en | ||||||
Article | ||||||
著者名(日) |
鈴木, 啓祐
× 鈴木, 啓祐 |
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著者名よみ |
スズキ, ケイスケ
× スズキ, ケイスケ |
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著者名(英) | ||||||
識別子Scheme | WEKO | |||||
識別子 | 8687 | |||||
姓名 | SUZUKI, KEISUKE | |||||
言語 | en | |||||
著者所属(日) | ||||||
流通経済大学 | ||||||
著者所属(英) | ||||||
en | ||||||
Ryutsu Keizai University | ||||||
抄録(英) | ||||||
内容記述タイプ | Other | |||||
内容記述 | In this paper, I proposed that when we define an augmented graph, minimax, maximin, maximum, and minimum points can be found in the graph and the dual augmented graph can be defined. The "augmented graph" is a graph obtained by addition of some vertices and edges to a given graph which is called "basic graph" in this paper. If the vertices in a basic graph are denoted by v_i (i=1, 2, …, m), those added to the basic graph by W_j (j=1, 2, …, n), and the length of the edge between vertices w_j and v_i by d_<ji>, the minimax, maximin, maximum, and minimum points are the points w_j's which have the lengths d_<ji>^*, d_<ji>^<**>, S^*, and S^<**> defined by d_<jt>^* = <min>___j <max>___i d_<jt> d_<ji>^<**> = <max>___j <min>___i d_<ji> S^* = <max>___j Σ^m__<i=1>d_<ji> S^<**> = <min>___j Σ^m__<i=1>d_<ji> respectively. And the dual augmented graph is the graph obtained by regarding the w_j's (j=1, 2, …, n) as the vertices in a new basic graph and the v_i's (i=1, 2, …, m) as the vertices added to the new basic graph. The minimax, maximin, maximum, and minimum points are the points v_i's which have the lengths d_<ij>^*, d_<ij>^<**>, S^*, and S^<**> denned by d_<ij>^* = <min>___i <max>___j d_<ij> d_<ij>^<**> = <max>___i <min>___j d_<ij> S^* = <max>___i Σ^n__<j=1> d_<ij> S^<**> = <min>___i Σ^n__<j=1> d_<ij> respectively. Incidentally, using augmented and the dual augmented graphs, I tried to examine the positions of the facilities for disposal of garbage in Tokyo. | |||||
雑誌書誌ID | ||||||
収録物識別子タイプ | NCID | |||||
収録物識別子 | AN00251278 | |||||
書誌情報 |
流通經濟大學論集 巻 11, 号 3, p. 1-24, 発行日 1977-01 |