"\u0410\u043B\u0433\u0435\u0431\u0440\u0438\u0447\u043D\u0430 \u0442\u0435\u043E\u0440\u0456\u044F \u0433\u0440\u0430\u0444\u0456\u0432 \u2014 \u043D\u0430\u043F\u0440\u044F\u043C\u043E\u043A \u0443 \u0442\u0435\u043E\u0440\u0456\u0457 \u0433\u0440\u0430\u0444\u0456\u0432, \u0449\u043E \u0437\u0430\u0441\u0442\u043E\u0441\u043E\u0432\u0443\u0454 \u0430\u043B\u0433\u0435\u0431\u0440\u0438\u0447\u043D\u0456 \u043C\u0435\u0442\u043E\u0434\u0438 \u0434\u043E \u0442\u0435\u043E\u0440\u0435\u0442\u0438\u043A\u043E-\u0433\u0440\u0430\u0444\u043E\u0432\u0438\u0445 \u0437\u0430\u0434\u0430\u0447 (\u043D\u0430 \u0434\u043E\u0434\u0430\u0447\u0443 \u0434\u043E , \u043A\u043E\u043C\u0431\u0456\u043D\u0430\u0442\u043E\u0440\u043D\u043E\u0433\u043E \u0442\u0430 \u0430\u043B\u0433\u043E\u0440\u0438\u0442\u043C\u0456\u0447\u043D\u043E\u0433\u043E \u043D\u0430\u043F\u0440\u044F\u043C\u043A\u0456\u0432). \u0423 \u0441\u0432\u043E\u044E \u0447\u0435\u0440\u0433\u0443, \u0430\u043B\u0433\u0435\u0431\u0440\u0438\u0447\u043D\u0430 \u0442\u0435\u043E\u0440\u0456\u044F \u0433\u0440\u0430\u0444\u0456\u0432 \u043F\u043E\u0434\u0456\u043B\u044F\u0454\u0442\u044C\u0441\u044F \u043D\u0430 \u0442\u0440\u0438 \u0433\u0456\u043B\u043A\u0438: \u043B\u0456\u043D\u0456\u0439\u043D\u043E-\u0430\u043B\u0433\u0435\u0431\u0440\u0438\u0447\u043D\u0443, \u0442\u0435\u043E\u0440\u0435\u0442\u0438\u043A\u043E-\u0433\u0440\u0443\u043F\u043E\u0432\u0443 \u0456 \u0432\u0438\u0432\u0447\u0430\u0454 \u0456\u043D\u0432\u0430\u0440\u0456\u0430\u043D\u0442\u0438 \u0433\u0440\u0430\u0444\u0456\u0432."@uk . "Teoria algebrica dei grafi"@it . . . . . "Algebraic graph theory is a branch of mathematics in which algebraic methods are applied to problems about graphs. This is in contrast to geometric, combinatoric, or algorithmic approaches. There are three main branches of algebraic graph theory, involving the use of linear algebra, the use of group theory, and the study of graph invariants."@en . . "\uB300\uC218\uC801 \uADF8\uB798\uD504 \uC774\uB860(\uC601\uC5B4: algebraic graph theory)\uC740 \uB300\uC218\uC801 \uBC29\uBC95\uC744 \uADF8\uB798\uD504\uC5D0 \uB300\uD55C \uBB38\uC81C\uC5D0 \uC801\uC6A9\uD558\uB294 \uC218\uD559\uC758 \uBD84\uC57C\uC774\uB2E4. \uC774\uAC83\uC740 \uAE30\uD558\uD559\uC801, \uC870\uD569\uB860\uC801 \uB610\uB294 \uC54C\uACE0\uB9AC\uC998\uC801\uC778 \uC811\uADFC \uBC29\uC2DD\uACFC \uB300\uC870\uB41C\uB2E4. \uB300\uC218\uC801 \uADF8\uB798\uD504 \uC774\uB860\uC5D0\uB294 \uC120\uD615\uB300\uC218\uD559, \uAD70\uB860\uC758 \uC751\uC6A9 \uBC0F \uC5F0\uAD6C \uB4F1 \uC138 \uAC00\uC9C0 \uC8FC\uC694 \uAC08\uB798\uAC00 \uC788\uB2E4."@ko . . . . . . "La teoria algebrica dei grafi \u00E8 una branca della matematica in cui si applicano metodi algebrici a problemi concernenti i grafi. Ci\u00F2 \u00E8 in contrasto con l'approccio geometrico, combinatorio o algoritmico. Ci sono tre branche principali della teoria algebrica dei grafi, che implicano l'uso dell'algebra lineare, l'uso della teoria dei gruppi e lo studio delle invarianti dei grafi."@it . . . . . . "1063362259"^^ . . "\u4EE3\u6570\u7684\u30B0\u30E9\u30D5\u7406\u8AD6\u306F\u3001\u30B0\u30E9\u30D5\u306B\u3064\u3044\u3066\u306E\u554F\u984C\u306B\u305F\u3044\u3057\u3066\u4EE3\u6570\u7684\u65B9\u6CD5\u304C\u9069\u7528\u3055\u308C\u308B\u3082\u306E\u3067\u3042\u308B\u3002\u3053\u308C\u306F\u3001\u7D44\u307F\u5408\u308F\u305B\u7684\u3001\u3082\u3057\u304F\u306F\u30A2\u30EB\u30B4\u30EA\u30BA\u30E0\u7684\u30A2\u30D7\u30ED\u30FC\u30C1\u3068\u306F\u5BFE\u7167\u7684\u3067\u3042\u308B\u3002\u305D\u308C\u305E\u308C\u3001\u7DDA\u5F62\u4EE3\u6570\u5B66\u306E\u5229\u7528\u3001\u7FA4\u8AD6\u306E\u5229\u7528\u3001\u304A\u3088\u3073\uFF08\u82F1\u8A9E: graph invariant\uFF09\u306E\u7814\u7A76\u3092\u542B\u3080\u3001\u4E3B\u3060\u3063\u305F\u4E09\u3064\u306E\u5206\u79D1\u304C\u3001\u4EE3\u6570\u7684\u30B0\u30E9\u30D5\u7406\u8AD6\u306B\u306F\u3042\u308B\u3002"@ja . . "6659"^^ . . . . . . . . . . "\u0410\u043B\u0433\u0435\u0431\u0440\u0438\u0447\u043D\u0430 \u0442\u0435\u043E\u0440\u0456\u044F \u0433\u0440\u0430\u0444\u0456\u0432"@uk . . . . . . . . . . . "Algebraic graph theory is a branch of mathematics in which algebraic methods are applied to problems about graphs. This is in contrast to geometric, combinatoric, or algorithmic approaches. There are three main branches of algebraic graph theory, involving the use of linear algebra, the use of group theory, and the study of graph invariants."@en . "\u4EE3\u6570\u7684\u30B0\u30E9\u30D5\u7406\u8AD6"@ja . "\u0410\u043B\u0433\u0435\u0431\u0440\u0430\u0438\u0447\u0435\u0441\u043A\u0430\u044F \u0442\u0435\u043E\u0440\u0438\u044F \u0433\u0440\u0430\u0444\u043E\u0432 \u2014 \u043D\u0430\u043F\u0440\u0430\u0432\u043B\u0435\u043D\u0438\u0435 \u0432 \u0442\u0435\u043E\u0440\u0438\u0438 \u0433\u0440\u0430\u0444\u043E\u0432, \u043F\u0440\u0438\u043C\u0435\u043D\u044F\u044E\u0449\u0435\u0435 \u0430\u043B\u0433\u0435\u0431\u0440\u0430\u0438\u0447\u0435\u0441\u043A\u0438\u0435 \u043C\u0435\u0442\u043E\u0434\u044B \u043A \u0442\u0435\u043E\u0440\u0435\u0442\u0438\u043A\u043E-\u0433\u0440\u0430\u0444\u043E\u0432\u044B\u043C \u0437\u0430\u0434\u0430\u0447\u0430\u043C (\u0432 \u0434\u043E\u043F\u043E\u043B\u043D\u0435\u043D\u0438\u0435 \u043A , \u043A\u043E\u043C\u0431\u0438\u043D\u0430\u0442\u043E\u0440\u043D\u043E\u043C\u0443 \u0438 \u0430\u043B\u0433\u043E\u0440\u0438\u0442\u043C\u0438\u0447\u0435\u0441\u043A\u043E\u043C\u0443 \u043D\u0430\u043F\u0440\u0430\u0432\u043B\u0435\u043D\u0438\u044F\u043C). \u0412 \u0441\u0432\u043E\u044E \u043E\u0447\u0435\u0440\u0435\u0434\u044C, \u0430\u043B\u0433\u0435\u0431\u0440\u0430\u0438\u0447\u0435\u0441\u043A\u0430\u044F \u0442\u0435\u043E\u0440\u0438\u044F \u0433\u0440\u0430\u0444\u043E\u0432 \u043F\u043E\u0434\u0440\u0430\u0437\u0434\u0435\u043B\u044F\u0435\u0442\u0441\u044F \u043D\u0430 \u0442\u0440\u0438 \u0432\u0435\u0442\u0432\u0438: \u043B\u0438\u043D\u0435\u0439\u043D\u043E-\u0430\u043B\u0433\u0435\u0431\u0440\u0430\u0438\u0447\u0435\u0441\u043A\u0443\u044E, \u0442\u0435\u043E\u0440\u0435\u0442\u0438\u043A\u043E-\u0433\u0440\u0443\u043F\u043F\u043E\u0432\u0443\u044E \u0438 \u0438\u0437\u0443\u0447\u0430\u044E\u0449\u0443\u044E \u0438\u043D\u0432\u0430\u0440\u0438\u0430\u043D\u0442\u044B \u0433\u0440\u0430\u0444\u043E\u0432."@ru . "\u4EE3\u6570\u56FE\u8BBA\uFF08algebraic graph theory\uFF09\u662F\u7528\u4EE3\u6570\u65B9\u6CD5\u5904\u7406\u56FE\u8BBA\u95EE\u9898\u7684\u6570\u5B66\u5206\u652F\u3002\u8FD9\u4E0D\u540C\u4E8E\u3001\u7EC4\u5408\u6216\u7B97\u6CD5\u7684\u65B9\u6CD5\u3002\u4EE3\u6570\u56FE\u8BBA\u6709\u4E09\u4E2A\u4E3B\u8981\u5206\u652F\uFF0C\u5206\u522B\u4F7F\u7528\u7EBF\u6027\u4EE3\u6570\uFF0C\u4F7F\u7528\u7FA4\u8BBA\uFF0C\u4EE5\u53CA\u7814\u7A76\u56FE\u4E0D\u53D8\u91CF\u3002"@zh . . . . "\uB300\uC218\uC801 \uADF8\uB798\uD504 \uC774\uB860(\uC601\uC5B4: algebraic graph theory)\uC740 \uB300\uC218\uC801 \uBC29\uBC95\uC744 \uADF8\uB798\uD504\uC5D0 \uB300\uD55C \uBB38\uC81C\uC5D0 \uC801\uC6A9\uD558\uB294 \uC218\uD559\uC758 \uBD84\uC57C\uC774\uB2E4. \uC774\uAC83\uC740 \uAE30\uD558\uD559\uC801, \uC870\uD569\uB860\uC801 \uB610\uB294 \uC54C\uACE0\uB9AC\uC998\uC801\uC778 \uC811\uADFC \uBC29\uC2DD\uACFC \uB300\uC870\uB41C\uB2E4. \uB300\uC218\uC801 \uADF8\uB798\uD504 \uC774\uB860\uC5D0\uB294 \uC120\uD615\uB300\uC218\uD559, \uAD70\uB860\uC758 \uC751\uC6A9 \uBC0F \uC5F0\uAD6C \uB4F1 \uC138 \uAC00\uC9C0 \uC8FC\uC694 \uAC08\uB798\uAC00 \uC788\uB2E4."@ko . . . "\u4EE3\u6570\u56FE\u8BBA"@zh . . "En math\u00E9matiques, la th\u00E9orie alg\u00E9brique des graphes utilise des m\u00E9thodes alg\u00E9briques pour r\u00E9soudre des probl\u00E8mes li\u00E9s aux graphes, par opposition \u00E0 des approches g\u00E9om\u00E9triques, combinatoires ou algorithmiques. On distingue trois branches principales au sein de la th\u00E9orie alg\u00E9briques des graphes, fond\u00E9es respectivement sur l'alg\u00E8bre lin\u00E9aire, la th\u00E9orie des groupes et l'\u00E9tude des invariants de graphe."@fr . "\uB300\uC218\uC801 \uADF8\uB798\uD504 \uC774\uB860"@ko . . . . "Teoria alg\u00E9brica dos grafos"@pt . "En math\u00E9matiques, la th\u00E9orie alg\u00E9brique des graphes utilise des m\u00E9thodes alg\u00E9briques pour r\u00E9soudre des probl\u00E8mes li\u00E9s aux graphes, par opposition \u00E0 des approches g\u00E9om\u00E9triques, combinatoires ou algorithmiques. On distingue trois branches principales au sein de la th\u00E9orie alg\u00E9briques des graphes, fond\u00E9es respectivement sur l'alg\u00E8bre lin\u00E9aire, la th\u00E9orie des groupes et l'\u00E9tude des invariants de graphe."@fr . . "\u4EE3\u6570\u56FE\u8BBA\uFF08algebraic graph theory\uFF09\u662F\u7528\u4EE3\u6570\u65B9\u6CD5\u5904\u7406\u56FE\u8BBA\u95EE\u9898\u7684\u6570\u5B66\u5206\u652F\u3002\u8FD9\u4E0D\u540C\u4E8E\u3001\u7EC4\u5408\u6216\u7B97\u6CD5\u7684\u65B9\u6CD5\u3002\u4EE3\u6570\u56FE\u8BBA\u6709\u4E09\u4E2A\u4E3B\u8981\u5206\u652F\uFF0C\u5206\u522B\u4F7F\u7528\u7EBF\u6027\u4EE3\u6570\uFF0C\u4F7F\u7528\u7FA4\u8BBA\uFF0C\u4EE5\u53CA\u7814\u7A76\u56FE\u4E0D\u53D8\u91CF\u3002"@zh . . . . . . . "1620216"^^ . "A teoria alg\u00E9brica dos grafos \u00E9 um ramo da matem\u00E1tica em que os m\u00E9todos alg\u00E9bricos s\u00E3o aplicados a problemas sobre grafos. Isso contrasta com as abordagens , combinat\u00F3rias ou algor\u00EDtmicas . Existem tr\u00EAs ramos principais da teoria de grafos alg\u00E9bricos, envolvendo o uso de \u00E1lgebra linear, o uso de teoria de grupos e o estudo de grafos invariantes."@pt . . . "Th\u00E9orie alg\u00E9brique des graphes"@fr . "\u0410\u043B\u0433\u0435\u0431\u0440\u0430\u0438\u0447\u0435\u0441\u043A\u0430\u044F \u0442\u0435\u043E\u0440\u0438\u044F \u0433\u0440\u0430\u0444\u043E\u0432"@ru . . . "\u0410\u043B\u0433\u0435\u0431\u0440\u0438\u0447\u043D\u0430 \u0442\u0435\u043E\u0440\u0456\u044F \u0433\u0440\u0430\u0444\u0456\u0432 \u2014 \u043D\u0430\u043F\u0440\u044F\u043C\u043E\u043A \u0443 \u0442\u0435\u043E\u0440\u0456\u0457 \u0433\u0440\u0430\u0444\u0456\u0432, \u0449\u043E \u0437\u0430\u0441\u0442\u043E\u0441\u043E\u0432\u0443\u0454 \u0430\u043B\u0433\u0435\u0431\u0440\u0438\u0447\u043D\u0456 \u043C\u0435\u0442\u043E\u0434\u0438 \u0434\u043E \u0442\u0435\u043E\u0440\u0435\u0442\u0438\u043A\u043E-\u0433\u0440\u0430\u0444\u043E\u0432\u0438\u0445 \u0437\u0430\u0434\u0430\u0447 (\u043D\u0430 \u0434\u043E\u0434\u0430\u0447\u0443 \u0434\u043E , \u043A\u043E\u043C\u0431\u0456\u043D\u0430\u0442\u043E\u0440\u043D\u043E\u0433\u043E \u0442\u0430 \u0430\u043B\u0433\u043E\u0440\u0438\u0442\u043C\u0456\u0447\u043D\u043E\u0433\u043E \u043D\u0430\u043F\u0440\u044F\u043C\u043A\u0456\u0432). \u0423 \u0441\u0432\u043E\u044E \u0447\u0435\u0440\u0433\u0443, \u0430\u043B\u0433\u0435\u0431\u0440\u0438\u0447\u043D\u0430 \u0442\u0435\u043E\u0440\u0456\u044F \u0433\u0440\u0430\u0444\u0456\u0432 \u043F\u043E\u0434\u0456\u043B\u044F\u0454\u0442\u044C\u0441\u044F \u043D\u0430 \u0442\u0440\u0438 \u0433\u0456\u043B\u043A\u0438: \u043B\u0456\u043D\u0456\u0439\u043D\u043E-\u0430\u043B\u0433\u0435\u0431\u0440\u0438\u0447\u043D\u0443, \u0442\u0435\u043E\u0440\u0435\u0442\u0438\u043A\u043E-\u0433\u0440\u0443\u043F\u043E\u0432\u0443 \u0456 \u0432\u0438\u0432\u0447\u0430\u0454 \u0456\u043D\u0432\u0430\u0440\u0456\u0430\u043D\u0442\u0438 \u0433\u0440\u0430\u0444\u0456\u0432."@uk . . . . . . . . "A teoria alg\u00E9brica dos grafos \u00E9 um ramo da matem\u00E1tica em que os m\u00E9todos alg\u00E9bricos s\u00E3o aplicados a problemas sobre grafos. Isso contrasta com as abordagens , combinat\u00F3rias ou algor\u00EDtmicas . Existem tr\u00EAs ramos principais da teoria de grafos alg\u00E9bricos, envolvendo o uso de \u00E1lgebra linear, o uso de teoria de grupos e o estudo de grafos invariantes."@pt . . . . . . "\u4EE3\u6570\u7684\u30B0\u30E9\u30D5\u7406\u8AD6\u306F\u3001\u30B0\u30E9\u30D5\u306B\u3064\u3044\u3066\u306E\u554F\u984C\u306B\u305F\u3044\u3057\u3066\u4EE3\u6570\u7684\u65B9\u6CD5\u304C\u9069\u7528\u3055\u308C\u308B\u3082\u306E\u3067\u3042\u308B\u3002\u3053\u308C\u306F\u3001\u7D44\u307F\u5408\u308F\u305B\u7684\u3001\u3082\u3057\u304F\u306F\u30A2\u30EB\u30B4\u30EA\u30BA\u30E0\u7684\u30A2\u30D7\u30ED\u30FC\u30C1\u3068\u306F\u5BFE\u7167\u7684\u3067\u3042\u308B\u3002\u305D\u308C\u305E\u308C\u3001\u7DDA\u5F62\u4EE3\u6570\u5B66\u306E\u5229\u7528\u3001\u7FA4\u8AD6\u306E\u5229\u7528\u3001\u304A\u3088\u3073\uFF08\u82F1\u8A9E: graph invariant\uFF09\u306E\u7814\u7A76\u3092\u542B\u3080\u3001\u4E3B\u3060\u3063\u305F\u4E09\u3064\u306E\u5206\u79D1\u304C\u3001\u4EE3\u6570\u7684\u30B0\u30E9\u30D5\u7406\u8AD6\u306B\u306F\u3042\u308B\u3002"@ja . . "La teoria algebrica dei grafi \u00E8 una branca della matematica in cui si applicano metodi algebrici a problemi concernenti i grafi. Ci\u00F2 \u00E8 in contrasto con l'approccio geometrico, combinatorio o algoritmico. Ci sono tre branche principali della teoria algebrica dei grafi, che implicano l'uso dell'algebra lineare, l'uso della teoria dei gruppi e lo studio delle invarianti dei grafi."@it . . . . . "Algebraic graph theory"@en . . . . 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