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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The -dimensional hypercube graph has vertex set and joins two vertices exactly when they differ in one coordinate. It is a -regular bipartite graph on vertices.