@article{oai:teapot.lib.ocha.ac.jp:00034623,
 author = {Hosoya, Haruo},
 issue = {2},
 journal = {お茶の水女子大學自然科學報告},
 month = {Jan},
 note = {application/pdf, 紀要論文, 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.},
 pages = {35--55},
 title = {Pell Equation. III. Graph-theoretical meaning of the solutions of the Pell equation through topological index Z},
 volume = {57},
 year = {2007}
}