Hypercube graph ( $Q_{d}$ )

The

d

-dimensional hypercube graph has vertex set

{0, 1}^{d}

and joins two vertices exactly when they differ in one coordinate. It is a

d

-regular bipartite graph on

2^{d}

vertices.

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- Gray code Hypercube graph

Gray code

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A Gray code orders binary strings so that successive strings differ in exactly one bit. Consequently it describes a path in a hypercube graph; a cyclic Gray code describes a cycle.

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A **hypercube graph**, often denoted as $ Q_n $, is a graph that represents the relationships between the vertices of an $ n $-dimensional hypercube. The vertices of the hypercube correspond to the binary strings of length $ n $, and there is an edge between two vertices if the corresponding binary strings differ in exactly one bit position.

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Hypercube graph ( $Q_{d}$ )

Gray code

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Hypercube graph (Qd​)

Gray code

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