The n-dimensional hypercube Q{sub}n is a graph that has N = 2{sup}n vertices and n2{sup}(n-1) edges. The vertices may be represented as the binary strings of length n. Two strings are considered adjacent if they differ in exactly one position. Alternatively, each binary string may be identified with a subset of {1,2,…,n}, with the string (x{sub}1,x{sub}2,…,x{sub}n) corresponding to the subset{i / x{sub}I=1}. Then two subsets are adjacent when their symmetric difference has exactly one element. If e is any edge joining vertices x and y, then the dimension of e is that integer i, 1 ≤i ≤ n such that x{sub}I≠ y{sub}i. Finding Hamiltonian paths (or cycles) in a hypercube has been the focus of many researchers, and many interesting properties of this popular topology have been discovered over the past lew decades [3]-[4]. One of the problems addressed in the literature is that of specifying Hamiltonian cycles in a hypercube. Enumeration of distinct Hamiltonian cycles in a hypercube is still an open problem, and only bounds on the number of such cycles are known [3]. For 0 ≤a ≤ b ≤ n, Q{sub}n(a, b) denotes the subgraph of Q{sub}n induced by the set of vertices x whose weight satisfies a≤wt(x)≤b. In a previous paper [1], for n= 2k+l, we proved that Q{sub}n(k, k+1) is Hamiltonian for 3 ≤ n ≤ 13. Also in another paper [2] for n >13 and 0展开▼
