What question did this study set out to answer?

Determine the optimal assignment of distinct integers to the vertices of an n-dimensional hypercube graph to minimize the total sum of absolute differences across adjacent vertices.

March 1, 1964Journal of the Society for Industrial and Applied Mathematics

Optimal Assignments of Numbers to Vertices

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Determine the optimal assignment of distinct integers to the vertices of an n-dimensional hypercube graph to minimize the total sum of absolute differences across adjacent vertices.
Formulated the vertex numbering problem mathematically within discrete graph theory.
Applied combinatorial optimization and edge-isoperimetric methods to analyze cut widths and vertex arrangements on n-cube graphs.
Established an exact numbering sequence that achieves the global minimum edge difference sum on hypercube vertices.
Derived foundational boundary conditions for graph layout, bandwidth minimization, and optimal digital data encoding.

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Implication

Theoretical analysis demonstrates optimal vertex numbering configurations on hypercubes, indicating foundational principles for data encoding and graph bandwidth minimization.

Cite This Study

L. H. Harper (1964) studied this question.

synapsesocial.com/papers/6a1da63e9aac5d9a645cbfd2 https://doi.org/10.1137/0112012

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Implication

Theoretical analysis demonstrates optimal vertex numbering configurations on hypercubes, indicating foundational principles for data encoding and graph bandwidth minimization.

Optimal Assignments of Numbers to Vertices

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Implication

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Optimal Assignments of Numbers to Vertices

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Implication

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