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# Hamiltonicity of Hypercubes and Generalized Hypercubes

Parallel algorithm in computer CPU with accordance to Hypercubes.

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### Preview of the essay: Hamiltonicity of Hypercubes and Generalized Hypercubes

Hamiltonicity of Hypercubes and Generalized Hypercubes I. 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 as parallel algorithms. 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. Hypercubes are special types of graphs. A graph G is an ordered triple (V(G), E(G), ...
... 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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