{"id":69065,"date":"2024-02-06T23:51:39","date_gmt":"2024-02-06T23:51:39","guid":{"rendered":"https:\/\/science-hub.click\/%E3%82%B9%E3%83%9A%E3%82%AF%E3%83%88%E3%83%AB%E3%82%B0%E3%83%A9%E3%83%95%E7%90%86%E8%AB%96%E3%81%AB%E3%81%A4%E3%81%84%E3%81%A6%E8%A9%B3%E3%81%97%E3%81%8F%E8%A7%A3%E8%AA%AC\/"},"modified":"2024-02-06T23:51:39","modified_gmt":"2024-02-06T23:51:39","slug":"%E3%82%B9%E3%83%9A%E3%82%AF%E3%83%88%E3%83%AB%E3%82%B0%E3%83%A9%E3%83%95%E7%90%86%E8%AB%96%E3%81%AB%E3%81%A4%E3%81%84%E3%81%A6%E8%A9%B3%E3%81%97%E3%81%8F%E8%A7%A3%E8%AA%AC","status":"publish","type":"post","link":"https:\/\/science-hub.click\/?p=69065","title":{"rendered":"\u30b9\u30da\u30af\u30c8\u30eb\u30b0\u30e9\u30d5\u7406\u8ad6\u306b\u3064\u3044\u3066\u8a73\u3057\u304f\u89e3\u8aac"},"content":{"rendered":"<div><div><h2>\u5c0e\u5165<\/h2><p><b>\u30b9\u30da\u30af\u30c8\u30eb \u30b0\u30e9\u30d5\u7406\u8ad6\u306f\u3001<\/b>\u30b0\u30e9\u30d5\u306e\u30b9\u30da\u30af\u30c8\u30eb\u3068\u305d\u306e\u30d7\u30ed\u30d1\u30c6\u30a3\u306e\u9593\u306e\u95a2\u4fc2\u306b\u7126\u70b9\u3092\u5f53\u3066\u3066\u304a\u308a\u3001\u4ee3\u6570\u30b0\u30e9\u30d5\u7406\u8ad6\u306e\u4e00\u90e8\u3067\u3059\u3002\u30b0\u30e9\u30d5\u306f\u8907\u6570\u306e\u884c\u5217\u3067\u8868\u3059\u3053\u3068\u304c\u3067\u304d\u3001\u884c\u5217\u306e\u56fa\u6709\u5024\u304c\u305d\u306e\u30b9\u30da\u30af\u30c8\u30eb\u3092\u69cb\u6210\u3057\u307e\u3059\u3002\u4e00\u822c\u306b\u3001\u96a3\u63a5\u884c\u5217\u3068\u6b63\u898f\u5316\u30e9\u30d7\u30e9\u30b7\u30a2\u30f3\u884c\u5217\u306b\u8208\u5473\u304c\u3042\u308a\u307e\u3059\u3002<\/p><figure class=\"wp-block-image size-large is-style-default\">\n<img decoding=\"async\" alt=\"\u30b9\u30da\u30af\u30c8\u30eb\u30b0\u30e9\u30d5\u7406\u8ad6\u306b\u3064\u3044\u3066\u8a73\u3057\u304f\u89e3\u8aac\" class=\"aligncenter\" onerror=\"this.style.display=none;\" src=\"https:\/\/img.youtube.com\/vi\/AuLeosWE7-Q\/0.jpg\" style=\"width:100%;\"\/><\/figure><h2>\u884c\u5217\u3068\u305d\u306e\u95a2\u4fc2<\/h2><p><span><a href=\"https:\/\/science-hub.click\/?p=41239\">\u30b0\u30e9\u30d5<\/a><\/span><span><i>G<\/i> = ( <i>V<\/i> , <i>E<\/i> )<\/span>\u306b\u3064\u3044\u3066\u8003\u3048\u307e\u3059\u3002\u3053\u3053\u3067\u3001 <span><i>V \u306f<\/i><\/span>\u9802\u70b9\u306e<span><a href=\"https:\/\/science-hub.click\/?p=57227\">\u30bb\u30c3\u30c8<\/a><\/span>\u3092\u793a\u3057\u3001 <span><i>E \u306f<\/i><\/span>\u30a8\u30c3\u30b8\u306e\u30bb\u30c3\u30c8\u3092\u793a\u3057\u307e\u3059\u3002\u30b0\u30e9\u30d5\u306b\u306f<span>| \u304c<\/span>\u3042\u308a\u307e\u3059\u3002 <span><i>V<\/i> | = <i>n<\/i><\/span>\u500b\u306e\u9802\u70b9\u3001\u3067\u793a\u3055\u308c\u308b<div class=\"math-formual notranslate\">$$ {s_1, \\cdots, s_n \\in S} $$<\/div>\u3068<span>| <i>E<\/i> | = <i>m \u500b\u306e<\/i><\/span>\u30a8\u30c3\u30b8\u3001\u3067\u793a\u3055\u308c\u308b<div class=\"math-formual notranslate\">$$ {e_{ij}, i \\in S, j \\in S} $$<\/div> \u3002\u30b0\u30e9\u30d5<span><i>G<\/i><\/span>\u306e\u96a3\u63a5\u884c\u5217<span><i>A<\/i><\/span>\u306e\u5404\u8981\u7d20\u306f\u6b21\u306e\u3088\u3046\u306b\u5b9a\u7fa9\u3055\u308c\u307e\u3059\u3002 <br\/><\/p><center><div class=\"math-formual notranslate\">$$ {a_{ij}=\\left\\{\\begin{array}{rl}  1 &amp; \\mbox{si } (v_i,v_j)\\in E \\\\         0 &amp; \\mbox{sinon.} \\end{array}\\right.} $$<\/div><\/center><div align=\"center\"><table><tr><th>\u30b0\u30e9\u30d5<\/th><th>\u96a3\u63a5\u884c\u5217\u306b\u3088\u308b\u8868\u73fe<\/th><th>\u30e9\u30d7\u30e9\u30b7\u30a2\u30f3\u884c\u5217\u306b\u3088\u308b\u8868\u73fe\uff08\u975e\u6b63\u898f\u5316\uff09<\/th><\/tr><tr><td> <figure class=\"wp-block-image size-large is-style-default\">\n<img decoding=\"async\" alt=\"6n-graf.svg\" class=\"aligncenter\" onerror=\"this.style.display=none;\" src=\"https:\/\/img.youtube.com\/vi\/PFcuUpBwgtE\/0.jpg\" style=\"width:100%;\"\/><\/figure> <\/td><td><center><div class=\"math-formual notranslate\">$$ {\\begin{pmatrix} 0 &amp; 1 &amp; 0 &amp; 0 &amp; 1 &amp; 0\\\\ 1 &amp; 0 &amp; 1 &amp; 0 &amp; 1 &amp; 0\\\\ 0 &amp; 1 &amp; 0 &amp; 1 &amp; 0 &amp; 0\\\\ 0 &amp; 0 &amp; 1 &amp; 0 &amp; 1 &amp; 1\\\\ 1 &amp; 1 &amp; 0 &amp; 1 &amp; 0 &amp; 0\\\\ 0 &amp; 0 &amp; 0 &amp; 1 &amp; 0 &amp; 0\\\\ \\end{pmatrix}} $$<\/div><\/center><\/td><td><center><div class=\"math-formual notranslate\">$$ {\\begin{pmatrix}  2 &amp; -1 &amp;  0 &amp;  0 &amp; -1 &amp;  0\\\\ -1 &amp;  3 &amp; -1 &amp;  0 &amp; -1 &amp;  0\\\\  0 &amp; -1 &amp;  2 &amp; -1 &amp;  0 &amp;  0\\\\  0 &amp;  0 &amp; -1 &amp;  3 &amp; -1 &amp; -1\\\\ -1 &amp; -1 &amp;  0 &amp; -1 &amp;  3 &amp;  0\\\\  0 &amp;  0 &amp;  0 &amp; -1 &amp;  0 &amp;  1\\\\ \\end{pmatrix}} $$<\/div><\/center><\/td><\/tr><\/table><\/div><p><i>\u6b21\u6570\u884c\u5217<\/i><span><i>D<\/i><\/span>\u306f<span><a href=\"https:\/\/science-hub.click\/?p=33864\">\u5bfe\u89d2\u884c\u5217<\/a><\/span>\u3067\u3001\u8981\u7d20<span><i>D<\/i> <sub><i>i<\/i> <i>i \u306f<\/i><\/sub><\/span>\u9802\u70b9<span><i>i<\/i><\/span>\u306e\u63a5\u7d9a<span><a href=\"https:\/\/science-hub.click\/?p=71097\">\u6570<\/a><\/span>\u3001\u3064\u307e\u308a\u305d\u306e<i>\u6b21\u6570<\/i>\u306b\u5bfe\u5fdc\u3057\u307e\u3059\u3002\u3053\u306e\u884c\u5217\u3068\u524d\u306e\u884c\u5217\u3092\u4f7f\u7528\u3057\u3066\u3001\u30e9\u30d7\u30e9\u30b7\u30a2\u30f3\u884c\u5217<span><i>L<\/i> = <i>D<\/i> \u2212 <i>A<\/i><\/span>\u3092\u5b9a\u7fa9\u3059\u308b\u3053\u3068\u3082\u3067\u304d\u307e\u3059\u3002\u305d\u306e\u6b63\u898f\u5316\u5f62\u5f0f<span><i>L<\/i> &#8216;<\/span>\u306f<span>\u3001 <i>L<\/i> &#8216; = <i>D<\/i> <sup>\u2212 1 \/ 2<\/sup> <i>L<\/i> <i>D<\/i> <sup>\u2212 1 \/ 2<\/sup> = <i>I<\/i> \u2212 <i>D<\/i> <sup>\u2212 1 \/ 2<\/sup> <i>A<\/i> <i>D<\/i> <sup>\u2212 1 \/ 2<\/sup><\/span>\u306b\u3088\u3063\u3066\u53d6\u5f97\u3057\u307e\u3059\u3002\u3053\u3053\u3067\u3001 <span><i>I \u306f<\/i><\/span><span><a href=\"https:\/\/science-hub.click\/?p=36866\">\u5358\u4f4d\u884c\u5217<\/a><\/span>\u3092\u793a\u3057\u307e\u3059\u3002\u307e\u305f\u306f\u3001\u76f4\u63a5\u53d6\u5f97\u3059\u308b\u3053\u3068\u3082\u3067\u304d\u307e\u3059\u3002\u5404\u8981\u7d20\u3054\u3068\u306b\u6b21\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002 <\/p><center><div class=\"math-formual notranslate\">$$ {\\ell_{i,j}:= \\begin{cases} 1 &amp; \\mbox{si}\\ i = j\\ \\mbox{et}\\ \\deg(v_i) \\neq 0\\\\ -\\frac{1}{\\sqrt{\\deg(v_i)\\deg(v_j)}} &amp; \\mbox{si}\\ i \\neq j\\ \\mbox{et}\\ v_i \\text{ est adjacent a } v_j \\\\ 0 &amp; \\text{sinon}. \\end{cases} } $$<\/div><\/center><p>\u6700\u5f8c\u306b\u3001\u30b0\u30e9\u30d5<span><i>G<\/i> = ( <i>V<\/i> , <i>E<\/i> )<\/span>\u306e\u51fa\u73fe\u884c\u5217<span><i>M<\/i><\/span>\u306f\u3001<span><a href=\"https:\/\/science-hub.click\/?p=84871\">\u6b21\u306e\u6b21\u5143<\/a><\/span>\u884c\u5217<span>|<\/span>\u306b\u306a\u308a\u307e\u3059\u3002 <span><i>V<\/i> | <i>\u00d7<\/i> | <i>E<\/i> |<\/span>\u3053\u3053\u3067\u3001\u9802\u70b9<span><i>v<\/i> <sub><i>i<\/i><\/sub><\/span>\u304c\u30a8\u30c3\u30b8<span><i>x<\/i> <sub><i>j<\/i><\/sub><\/span>\u306e\u7aef\u70b9\u3067\u3042\u308b\u5834\u5408\u3001\u30a8\u30f3\u30c8\u30ea<span><i>b<\/i> <sub><i>i<\/i> <i>j<\/i><\/sub><\/span>\u306f 1\u3001\u305d\u3046\u3067\u306a\u3044\u5834\u5408\u306f 0 \u3067\u3059\u3002\u6b21\u306e\u4e00\u9023\u306e\u95a2\u4fc2\u304c\u3042\u308a\u307e\u3059\u3002\u3053\u3053\u3067\u3001 <span><i>I \u306f<\/i><\/span>\u5358\u4f4d\u884c\u5217\u3092\u793a\u3057\u307e\u3059\u3002<\/p><ul><li> <span><i>A<\/i> = <i>M<\/i> <i>M<\/i> <sup><i>T<\/i><\/sup> \u2212 <i>D<\/i><\/span><\/li><li>\u6298\u308c\u7dda\u30b0\u30e9\u30d5<span><i>L<\/i> ( <i>G<\/i> )<\/span>\u306e\u96a3\u63a5\u884c\u5217\u306e\u5834\u5408\u3001 <span><i>A<\/i> = <i>M<\/i> <sup><i>T<\/i><\/sup> <i>M<\/i> \u2212 2 <i>I<\/i><\/span><\/li><li>\u7d30\u5206\u30b0\u30e9\u30d5<span><i>S<\/i> ( <i>G<\/i> )<\/span>\u306e\u96a3\u63a5\u884c\u5217\u306e\u5834\u5408\u3001 <div class=\"math-formual notranslate\">$$ {A = \\begin{pmatrix} 0 &amp;M^T\\\\ M &amp; 0\\\\ \\end{pmatrix}} $$<\/div><\/li><\/ul><p>\u884c\u5217\u306e<i>\u30b9\u30da\u30af\u30c8\u30eb<\/i>\u306f\u305d\u306e\u56fa\u6709\u5024\u306e\u30bb\u30c3\u30c8\u3067\u3059<div class=\"math-formual notranslate\">$$ {\\lambda_0 \\le \\lambda_1 \\le \\cdots \\le \\lambda_{n-1}} $$<\/div> ;\u62e1\u5f35\u3057\u3066\u3001\u30b0\u30e9\u30d5\u306e\u30b9\u30da\u30af\u30c8\u30eb\u306b\u3064\u3044\u3066\u8a71\u3057\u307e\u3059\u3002<span>\u56fa\u6709\u5024<\/span><span>\u03bb<\/span>\u306e<i>\u4ee3\u6570\u7684\u591a\u91cd\u5ea6\u306f<\/i>\u3001 <span><a href=\"https:\/\/science-hub.click\/?p=108981\">\u7279\u6027\u591a\u9805\u5f0f<\/a><\/span>\u306e<span><a href=\"https:\/\/science-hub.click\/?p=23938\">\u5358\u9805\u5f0f<\/a><\/span><span>( <i>X<\/i> \u2212 \u03bb)<\/span>\u306e<span><a href=\"https:\/\/science-hub.click\/?p=15958\">\u3079\u304d\u4e57<\/a><\/span>(<i>\u3064\u307e\u308a\u3001<\/i>\u7279\u6027<span><a href=\"https:\/\/science-hub.click\/?p=35323\">\u591a\u9805\u5f0f<\/a><\/span>\u306e\u6839\u306e\u591a\u91cd\u5ea6) \u3067\u3042\u308b\u3053\u3068\u3092\u601d\u3044\u51fa\u3057\u3066\u304f\u3060\u3055\u3044\u3002\u7279\u6027\u591a\u9805\u5f0f\u3092\u5909\u66f4\u3057\u3066\u3001\u30b0\u30e9\u30d5\u306e\u4ed6\u306e\u7279\u6027\u3092\u8003\u616e\u3059\u308b\u3053\u3068\u3082\u53ef\u80fd\u3067\u3059\u3002\u30c7\u30d5\u30a9\u30eb\u30c8\u3067\u306f\u3001\u591a\u9805\u5f0f<span><i>P<\/i> <sub><i>G<\/i><\/sub> (\u03bb) = |<\/span>\u3092\u8003\u616e\u3057\u307e\u3059\u3002 <span>\u03bb <i>I<\/i> \u2212 <i>A<\/i> |<\/span> \u3001\u305f\u3060\u3057\u3001 <span><i>R<\/i> <sub><i>G<\/i><\/sub> (\u03bb) = |<\/span>\u306a\u3069\u306e\u5909\u5f62\u306b\u3082\u8208\u5473\u304c\u3042\u308b\u304b\u3082\u3057\u308c\u307e\u305b\u3093\u3002 <span>\u03bb <i>I<\/i> \u2212 <i>D<\/i> \u2212 <i>A<\/i> |<\/span>\u307e\u305f\u306f<span><i>Q<\/i> <sub><i>G<\/i><\/sub> (\u03bb) = | <i>D<\/i> | <sup>\u2212 1<\/sup> * | \u03bb <i>D<\/i> \u2212 <i>A<\/i> |<\/span> \u3002<\/p><h2>\u6b63\u898f\u5316\u3055\u308c\u305f\u30e9\u30d7\u30e9\u30b7\u30a2\u30f3\u884c\u5217\u306e\u30b9\u30da\u30af\u30c8\u30eb<\/h2><p>\u56fa\u6709\u5024<span>\u03bb <sub>1 \u306f<\/sub><\/span>\u3001\u30b0\u30e9\u30d5\u306e<b>\u4ee3\u6570\u7684\u63a5\u7d9a\u6027<\/b>\u3068\u547c\u3070\u308c\u307e\u3059\u3002\u30b9\u30da\u30af\u30c8\u30eb\u306e\u91cd\u8981\u306a\u7279\u6027\u3092\u4ee5\u4e0b\u306b\u307e\u3068\u3081\u307e\u3059\u3002<\/p><ul><li> <span><sub>\u03bb0<\/sub> = 0<\/span> \u3002 <\/li><li><div class=\"math-formual notranslate\">$$ {\\sum_i \\lambda_i \\le n} $$<\/div>\u30b0\u30e9\u30d5\u304c\u3064\u306a\u304c\u3063\u3066\u3044\u308b\u5834\u5408\u3002<\/li><li>\u3082\u3057<div class=\"math-formual notranslate\">$$ {n \\ge 2} $$<\/div>\u305d\u3057\u3066 G \u304c\u5b8c\u5168\u306a\u30b0\u30e9\u30d5\u3067\u3042\u308b\u3068\u3059\u308b\u3068\u3001 <div class=\"math-formual notranslate\">$$ {\\lambda_1 = \\frac{n}{n-1}} $$<\/div> \u3001 \u3055\u3082\u306a\u3044\u3068<div class=\"math-formual notranslate\">$$ {\\lambda_1 \\le 1} $$<\/div> \u3002<\/li><li>\u30b0\u30e9\u30d5\u304c\u63a5\u7d9a\u3055\u308c\u3066\u3044\u308b\u5834\u5408\u306f\u3001 <span>\u03bb <sub>1<\/sub> &gt; 0 \u306b<\/span>\u306a\u308a\u307e\u3059\u3002 <span>\u03bb <sub><i>i<\/i><\/sub> = 0<\/span>\u306e\u5834\u5408\u3001 <div class=\"math-formual notranslate\">$$ {\\lambda_{i+1} \\neq 0} $$<\/div>\u3053\u306e\u5834\u5408\u3001 <span><i>G \u306f<\/i><\/span>\u6b63\u78ba\u306b<span><i>i<\/i> + 1 \u500b\u306e<\/span>\u30b3\u30f3\u30dd\u30fc\u30cd\u30f3\u30c8 (<i>\u3064\u307e\u308a\u3001<\/i>\u63a5\u7d9a\u3055\u308c\u305f\u30b0\u30e9\u30d5) \u3092\u6301\u3061\u307e\u3059\u3002 <\/li><li><div class=\"math-formual notranslate\">$$ {\\lambda_i \\le 2} $$<\/div><div class=\"math-formual notranslate\">$$ {\\forall i \\le n &#8211; 1} $$<\/div> \u3002<\/li><\/ul><p>\u3053\u306e\u884c\u5217\u306e\u4ed6\u306e\u30d7\u30ed\u30d1\u30c6\u30a3\u306e\u4e2d\u3067\u3082\u3001\u305d\u306e\u884c\u5217\u5f0f\u306f\u30b0\u30e9\u30d5\u5185\u306e\u30b9\u30d1\u30cb\u30f3\u30b0 \u30c4\u30ea\u30fc\u306e\u6570\u3092\u4e0e\u3048\u307e\u3059\u3002<\/p><figure class=\"wp-block-image size-large is-style-default\">\n<img decoding=\"async\" alt=\"\u30b9\u30da\u30af\u30c8\u30eb\u30b0\u30e9\u30d5\u7406\u8ad6\u306b\u3064\u3044\u3066\u8a73\u3057\u304f\u89e3\u8aac\" class=\"aligncenter\" onerror=\"this.style.display=none;\" src=\"https:\/\/img.youtube.com\/vi\/b_XFzl4YGFs\/0.jpg\" style=\"width:100%;\"\/><\/figure><h2>\u96a3\u63a5\u884c\u5217\u30b9\u30da\u30af\u30c8\u30eb<\/h2><p>\u30b0\u30e9\u30d5\u884c\u5217\u306f\u6b63\u3067\u3042\u308a\u3001\u30b0\u30e9\u30d5\u304c\u3064\u306a\u304c\u3063\u3066\u3044\u308b\u5834\u5408\u306f\u6e1b\u3089\u3059\u3053\u3068\u304c\u3067\u304d\u307e\u305b\u3093\u3002\u7121\u5411\u30b0\u30e9\u30d5\u306e\u5834\u5408\u3001\u884c\u5217\u306f\u5bfe\u79f0\u304b\u3064\u30a8\u30eb\u30df\u30fc\u30c8\u884c\u5217\u3067\u3059\u3002\u3064\u307e\u308a\u3001 <div class=\"math-formual notranslate\">$$ {A^\\dagger = A} $$<\/div>\u307e\u305f\u306f<div class=\"math-formual notranslate\">$$ {A^\\dagger} $$<\/div>\u306f<span><i>A<\/i><\/span>\u306e\u968f\u4f34\u884c\u5217\u3067\u3059\u3002\u884c\u5217\u306e<span><a href=\"https:\/\/science-hub.click\/?p=59617\">\u30c8\u30ec\u30fc\u30b9<\/a><\/span>\u306f\u30eb\u30fc\u30d7\u6570\u306e 2 \u500d\u306b\u7b49\u3057\u304f\u306a\u308a\u307e\u3059\u3002\u5b9f\u969b\u3001<span><a href=\"https:\/\/science-hub.click\/?p=100875\">\u5bfe\u89d2\u7dda<\/a><\/span>\u4e0a\u306e\u8981\u7d20\u306f\u30eb\u30fc\u30d7\u306e\u5b58\u5728\u3092\u793a\u3057\u3001\u30c8\u30ec\u30fc\u30b9\u306f\u3053\u308c\u3089\u306e\u8981\u7d20\u306e\u5408\u8a08\u3067\u3059\u3002\u6b21\u306e\u3088\u3046\u306a\u30d7\u30ed\u30d1\u30c6\u30a3\u304c\u3042\u308a\u307e\u3059\u3002<\/p><ul><li>\u884c\u5217\u306e\u30b9\u30da\u30af\u30c8\u30eb\u534a\u5f84<span>\u03c1( <i>A<\/i> )<\/span> \u3001\u3064\u307e\u308a\u6700\u5927\u56fa\u6709\u5024\u306f\u6b21\u306e\u6761\u4ef6\u3092\u6e80\u305f\u3057\u307e\u3059\u3002 <div class=\"math-formual notranslate\">$$ {2 \\cdot \\cos(\\frac{\\pi}{n + 1}) \\le \\rho (A) \\le n &#8211; 1} $$<\/div>\u63a5\u7d9a\u3055\u308c\u305f\u30b0\u30e9\u30d5\u306e\u5834\u5408\u3002\u30d1\u30b9\u306e\u5834\u5408\u306f\u4e0b\u9650\u306b\u5230\u9054\u3057\u3001\u5b8c\u5168\u306a\u30b0\u30e9\u30d5\u3067\u306f\u4e0a\u9650\u306b\u5230\u9054\u3057\u307e\u3059\u3002<\/li><li>\u30b0\u30e9\u30d5\u304c<span><i>k<\/i><\/span>\u6b63\u5247\u306e\u5834\u5408\u3001 <span>\u03c1( <i>A<\/i> ) = <i>k<\/i><\/span>\u3068\u306a\u308a\u3001 <span>\u03c1( <i>A<\/i> )<\/span>\u306e\u591a\u91cd\u5ea6\u304c\u9023\u7d50\u6210\u5206\u306e\u6570\u3092\u4e0e\u3048\u307e\u3059\u3002<\/li><li>\u30b0\u30e9\u30d5\u306b\u30b5\u30a4\u30af\u30eb\u304c\u542b\u307e\u308c\u3066\u3044\u306a\u3044\u5834\u5408\u306b\u9650\u308a\u3001\u3059\u3079\u3066\u306e\u56fa\u6709\u5024\u306f\u30bc\u30ed\u306b\u306a\u308a\u307e\u3059\u3002<\/li><li> <span>\u2212 \u03c1( <i>A<\/i> )<\/span>\u3082\u56fa\u6709\u5024\u3067\u3042\u308b\u5834\u5408\u3001\u30b0\u30e9\u30d5\u306b\u306f\u5947\u6570<span><a href=\"https:\/\/science-hub.click\/?p=17420\">\u9577<\/a><\/span>\u30b5\u30a4\u30af\u30eb\u306e\u307f\u304c\u542b\u307e\u308c\u307e\u3059\u3002<\/li><li> <span><i>k \u500b\u306e<\/i><\/span>\u7570\u306a\u308b\u56fa\u6709\u5024\u304c\u3042\u308b\u5834\u5408\u3001<span><a href=\"https:\/\/science-hub.click\/?p=109019\">\u76f4\u5f84<\/a><\/span><span><i>D \u306f<\/i><\/span>\u6b21\u306e\u6761\u4ef6\u3092\u6e80\u305f\u3057\u307e\u3059\u3002 <div class=\"math-formual notranslate\">$$ {D \\le m &#8211; 1} $$<\/div> \u3002<\/li><li>\u6700\u5927\u5b89\u5b9a\u306e\u30b5\u30a4\u30ba<span><i>t<\/i><\/span>\u306f\u6b21\u306e\u6761\u4ef6\u3092\u6e80\u305f\u3057\u307e\u3059\u3002 <div class=\"math-formual notranslate\">$$ {t \\le p_0 + min(p_-,p_+)} $$<\/div>\u3053\u3053\u3067\u3001 <span><i>p<\/i> <sub>\u2212<\/sub> \u3001 <i>p<\/i> <sub>0<\/sub> \u3001 <i>p<\/i> <sub>+ \u306f<\/sub><\/span>\u305d\u308c\u305e\u308c\u30010 \u4ee5\u4e0a\u306e\u5c0f\u3055\u3044\u56fa\u6709\u5024\u306e\u6570\u3067\u3059\u3002 <\/li><li><div class=\"math-formual notranslate\">$$ {\\frac{\\rho(A)}{-q} + 1 \\le \\chi(G) \\le \\rho(A) + 1} $$<\/div>\u3053\u3053\u3067\u3001 <span>\u03c7( <i>G<\/i> )<\/span>\u306f\u8272\u5f69\u6570\u3001 <span><i>q \u306f<\/i><\/span>\u6700\u5c0f\u306e\u56fa\u6709\u5024\u3067\u3059\u3002<\/li><\/ul><\/div><h2 class=\"ref_link\">\u53c2\u8003\u8cc7\u6599<\/h2><ol><li><a class=\"notranslate\" href=\"https:\/\/ca.wikipedia.org\/wiki\/Teoria_espectral_de_grafs\">Teoria espectral de grafs \u2013 catalan<\/a><\/li><li> <a class=\"notranslate\" href=\"https:\/\/de.wikipedia.org\/wiki\/Spektrale_Graphentheorie\">Spektrale Graphentheorie \u2013 allemand<\/a><\/li><li> <a class=\"notranslate\" href=\"https:\/\/en.wikipedia.org\/wiki\/Spectral_graph_theory\">Spectral graph theory \u2013 anglais<\/a><\/li><li> <a class=\"notranslate\" href=\"https:\/\/es.wikipedia.org\/wiki\/Teor%C3%ADa_espectral_de_grafos\">Teor\u00eda espectral de grafos \u2013 espagnol<\/a><\/li><li> <a class=\"notranslate\" href=\"https:\/\/fa.wikipedia.org\/wiki\/%D9%86%D8%B8%D8%B1%DB%8C%D9%87_%D8%B7%DB%8C%D9%81%DB%8C_%DA%AF%D8%B1%D8%A7%D9%81%E2%80%8C%D9%87%D8%A7\">\u0646\u0638\u0631\u06cc\u0647 \u0637\u06cc\u0641\u06cc \u06af\u0631\u0627\u0641\u200c\u0647\u0627 \u2013 persan<\/a><\/li><li> <a class=\"notranslate\" href=\"https:\/\/hu.wikipedia.org\/wiki\/Spektr%C3%A1lis_gr%C3%A1felm%C3%A9let\">Spektr\u00e1lis gr\u00e1felm\u00e9let \u2013 hongrois<\/a><\/li><\/ol><\/div>\n<div class=\"feature-video\">\n <h2>\n  \u30b9\u30da\u30af\u30c8\u30eb\u30b0\u30e9\u30d5\u7406\u8ad6\u306b\u3064\u3044\u3066\u8a73\u3057\u304f\u89e3\u8aac\u30fb\u95a2\u9023\u52d5\u753b\n <\/h2>\n <div class=\"video-item\">\n  \n  <figure class=\"wp-block-embed is-type-video is-provider-youtube wp-block-embed-youtube wp-embed-aspect-16-9 wp-has-aspect-ratio\">\n   <div class=\"wp-block-embed__wrapper\">\n    <iframe loading=\"lazy\" title=\"\u30b0\u30e9\u30d5\u7406\u8ad6\u2460(\u4e00\u7b46\u66f8\u304d\u306e\u5b9a\u7406)\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/PFcuUpBwgtE?feature=oembed\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share\" referrerpolicy=\"strict-origin-when-cross-origin\" allowfullscreen><\/iframe>\n   <\/div>\n  <\/figure>\n  \n <\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>\u5c0e\u5165 \u30b9\u30da\u30af\u30c8\u30eb \u30b0\u30e9\u30d5\u7406\u8ad6\u306f\u3001\u30b0\u30e9\u30d5\u306e\u30b9\u30da\u30af\u30c8\u30eb\u3068\u305d\u306e\u30d7\u30ed\u30d1\u30c6\u30a3\u306e\u9593\u306e\u95a2\u4fc2\u306b\u7126\u70b9\u3092\u5f53\u3066\u3066\u304a\u308a\u3001\u4ee3\u6570\u30b0\u30e9\u30d5\u7406\u8ad6\u306e\u4e00\u90e8\u3067\u3059\u3002\u30b0\u30e9\u30d5\u306f\u8907\u6570\u306e\u884c\u5217\u3067\u8868\u3059\u3053\u3068\u304c\u3067\u304d\u3001\u884c\u5217\u306e\u56fa\u6709\u5024\u304c\u305d\u306e\u30b9\u30da\u30af\u30c8\u30eb\u3092\u69cb\u6210\u3057\u307e\u3059\u3002\u4e00\u822c\u306b\u3001\u96a3\u63a5\u884c\u5217\u3068\u6b63 [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":69066,"comment_status":"","ping_status":"","sticky":false,"template":"","format":"standard","meta":{"fifu_image_url":"https:\/\/img.youtube.com\/vi\/X1AsMlJdiok\/0.jpg","fifu_image_alt":"\u30b9\u30da\u30af\u30c8\u30eb\u30b0\u30e9\u30d5\u7406\u8ad6\u306b\u3064\u3044\u3066\u8a73\u3057\u304f\u89e3\u8aac","footnotes":""},"categories":[5],"tags":[64082,12027,11,13,14,10,64083,12,8,391,16,15,9],"class_list":["post-69065","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-dictionary","tag-fonction-affine","tag-spectrale","tag-techniques","tag-technologie","tag-news","tag-actualite","tag-hedera","tag-dossier","tag-definition","tag-theorie","tag-sciences","tag-article","tag-explications"],"_links":{"self":[{"href":"https:\/\/science-hub.click\/index.php?rest_route=\/wp\/v2\/posts\/69065"}],"collection":[{"href":"https:\/\/science-hub.click\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/science-hub.click\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/science-hub.click\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/science-hub.click\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=69065"}],"version-history":[{"count":0,"href":"https:\/\/science-hub.click\/index.php?rest_route=\/wp\/v2\/posts\/69065\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/science-hub.click\/index.php?rest_route=\/wp\/v2\/media\/69066"}],"wp:attachment":[{"href":"https:\/\/science-hub.click\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=69065"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/science-hub.click\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=69065"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/science-hub.click\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=69065"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}