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Hypercubes and Generalized Hypercubes

Many problems can be solved much faster using parallel computers rather than serial computers. One model for parallel computations is known as the n-cube or the hypercube. This paper presents the hamiltonicity of hypercubes and generalized hypercubes

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Preview of the essay: Hypercubes and Generalized Hypercubes

Hypercubes and Generalized Hypercubes and Their Hamiltonicity Introduction The traditional computer, often called a serial computer, executes one instruction at a time. The definition of algorithm, in this paper, assumes that one instruction is executed at a time. Such algorithms are called serial algorithms. Recently, it is feasible to build parallel computers, which have many processors that are capable of executing several instructions at a time. The associated algorithms are known ...

... also means that Qk+1,k is connected.
Thus, if k is odd then Qn,k is connected, n > k.

III. Hamiltonicity of the Generalized Hypercube Qn,k

Since Qn,k is connected if and only if k is odd and our concern is on the hamiltonicity of the generalized hypercube, Qn,k, then we only concentrate on the Qn,k’s where k is odd.
We state the next theorem without proof.

Theorem 12. Qn,k is hamiltonian if and only if n > k and k is odd.

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