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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 |
|---|---|---|
KJ00004830818.pdf (857.4 kB)
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| Item type | 紀要論文 / Departmental Bulletin Paper(1) | |||||
|---|---|---|---|---|---|---|
| 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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| ISSN | ||||||
| 収録物識別子タイプ | ISSN | |||||
| 収録物識別子 | 00298190 | |||||
| 書誌レコードID | ||||||
| 収録物識別子タイプ | NCID | |||||
| 収録物識別子 | AN00033958 | |||||
| フォーマット | ||||||
| 内容記述タイプ | Other | |||||
| 内容記述 | application/pdf | |||||
| 形態 | ||||||
| 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 | ||||||
