@article{oai:teapot.lib.ocha.ac.jp:00034614,
 author = {Hosoya, Haruo},
 issue = {1},
 journal = {お茶の水女子大學自然科學報告},
 month = {Sep},
 note = {application/pdf, 紀要論文, Manipulation of continued fraction, either finite and infinite, was shown to be greatly simplified and systematized by introducing the topological index Z and caterpillar graph. The continuant which was introduced by Euler in 18 century for solving continued fraction problems was shown to be identical to the Z-index of the caterpillar graph derived from the continued fraction concerned. Then the fastest algorithm for solving the Pell equations was obtained. Further, graph-theoretical interpretation for Fibonacci and Lucas numbers, and generalized Fibonacci numbers was obtained.},
 pages = {15--28},
 title = {Continuant, caterpillar, and topological index Z. Fastest algorithm for degrading a continued fraction},
 volume = {58},
 year = {2007}
}