用广义斐波那契数及其产生方法进行图的哈密顿圈的计数
ENUMERATING ALL HAMILTONIAN CYCLES IN SOME GRAPHS BY USING THE GENERALIZED FIBONACCI SEQUENCE AND ITS PRODUCTION RULE
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摘要: 本文首先对斐波那契数进行推广,然后对文献[1]中提出的递推算法进行了抽象,找到了可以描述这一算法的产生式和递推关系,从而首次求得了两种最大平面图中哈密顿圈的计数公式。
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关键词:
Abstract: In this paper the Fibonacci sequence is generalized at first. Then the algorithm which has been published in this Journal by the author and his colleague is developed. Both production and recursion formulas for describing the algorithm are obtained. Here the two formulas for enumerating all hamiltonian cycles in two kinds of maxi-mum planar graphs seem to be derived for the first time. -
金绥更、江炳尧,电子学通讯,4(1982), 191.[2]F. Harary著,李慰萱译,图论,上海科技出版社,1980.[4]D. E. Knuth著,管纪文、苏运霖译,计算机程序设计技巧,国防工业出版社,1980.[8]S. L. Hakimi and E. F. Schmeichel, J. of Graph Theory, 3(1979),69. -
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