遞迴式循環圖G(N, d)是Park和Chwa [14]在1994年提出的。G(N, d)是含有N個頂點且距離為d的乘羃的點相連而形成的循環圖。對於任意非負整數n，G(2*n, 4)是遞迴式循環圖的一個特殊子家族，擁有直徑和路徑組織等良好的特性，可以應用在多元網路的結構裡。本篇論文中，我們將探討G(2*n, 4)中相互獨立的漢米爾頓環路。
G(2*n, 4)和超立方體Qn有相同的維度n，但卻有較小的直徑[21]。當n屬於{1, 2, 3}時，Qn上有n-1條相互獨立的漢米爾頓環路；當n大於等於4時，則有n條相互獨立的漢米爾頓環路。由於G(2*n, 4)和Qn有許多類似的特性，例如G(2*n, 4)可以嵌入Qn中[15]。據此，我們將推論出G(2*n, 4)中相互獨立漢米爾頓環路的數目。在本篇論文中，我們證明了在G(2*n, 4)上，有n條相互獨立漢米的漢米爾頓環路。

The recursive circulant graphs G(N, d), have been introduced in 1994 [14], are circulant graphs with N nodes and with jumps of powers of d. The subfamily of the recursive circulant graphs of the form G(2*n, 4), for some nonnegative integer n, was also presented as a new topology for multicomputer networks because of its nice properties concerning their diameter and routing schemes, and so on.
In this paper, we study the mutually independent hamiltonian cycles of the recursive circulant graphs
G(2*n, 4). The recursive circulant graphs G(2*n, 4) and the hypercubes Qn have many similar properties. For examples,
G(2*n, 4) have the same degree as Qn of dimension n, but have a smaller diameter [21]；G(2*n, 4) have the relationship with Qn in terms of embedding [15]. Furthermore, it has been shown that the numbers of the mutually independent hamiltonian cycles of Qn are
MIHC(Qn) = n-1 if n belongs to {1, 2, 3}；
= n if n is bigger and equal to4.
Therefore, we would guess the numbers of the mutually independent hamiltonian cycles of the recursive circulant graphs G(2*n, 4), and then have verified the results that there are n mutually independent hamiltonian cycles in
G(2*n, 4), for n is bigger and equal to3.

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