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Pell Equation. III. Graph-theoretical meaning of the solutions of the Pell equation through topological index Z
http://hdl.handle.net/10083/2404
http://hdl.handle.net/10083/2404efd7538d-097c-4b92-a281-ec3825b093b0
名前 / ファイル | ライセンス | アクション |
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Item type | 紀要論文 / Departmental Bulletin Paper(1) | |||||
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公開日 | 2008-04-30 | |||||
タイトル | ||||||
タイトル | Pell Equation. III. Graph-theoretical meaning of the solutions of the Pell equation through topological index Z | |||||
言語 | ||||||
言語 | eng | |||||
資源タイプ | ||||||
資源 | http://purl.org/coar/resource_type/c_6501 | |||||
タイプ | departmental bulletin paper | |||||
著者 |
Hosoya, Haruo
× Hosoya, Haruo |
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著者(ヨミ) | ||||||
識別子Scheme | WEKO | |||||
識別子 | 70917 | |||||
姓名 | ホソヤ, ハルオ | |||||
内容記述 | ||||||
内容記述タイプ | Other | |||||
内容記述 | For a non-directed graph G composed of vertices and edges the topological index Z_G has been defined by the present author as the total sum of perfect and imperfect matchings. The Z_G values of several typical series of graphs have been known to be equal to Fibonacci, Lucas, and Pell numbers. In this paper the solutions of Pell equation x^2-Dy^2=±N for special values of D with N=1 and 4 are shown to give these series of numbers, which means that this is the first graphical or graph-theoretical interpretation of the solutions of Pell equation. In this analysis the Chebyshev polynomials of the first and second kinds, T_n and U_n, together with their modified version, C_n and S_n, are involved. For any D with N=1 and 4, there were found certain series of graphs whose Z_G values just represent the solutions of Pell equation. | |||||
書誌情報 |
お茶の水女子大學自然科學報告 巻 57, 号 2, p. 35-55, 発行日 2007-01 |
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収録物識別子タイプ | ISSN | |||||
収録物識別子 | 00298190 | |||||
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収録物識別子タイプ | NCID | |||||
収録物識別子 | AN00033958 | |||||
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内容記述タイプ | Other | |||||
内容記述 | application/pdf | |||||
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857405 bytes | ||||||
日本十進分類法 | ||||||
主題Scheme | NDC | |||||
主題 | 400 | |||||
出版者 | ||||||
出版者 | お茶の水女子大学 | |||||
資源タイプ | ||||||
内容記述タイプ | Other | |||||
内容記述 | 紀要論文 | |||||
資源タイプ・ローカル | ||||||
紀要論文 | ||||||
資源タイプ・NII | ||||||
Departmental Bulletin Paper | ||||||
資源タイプ・DCMI | ||||||
text | ||||||
資源タイプ・ローカル表示コード | ||||||
03 |