High Quality Content by WIKIPEDIA articles! In graph theory, a partial cube is a graph that is an isometric subgraph of a hypercube. In other words, a partial cube is a subgraph of a hypercube that preserves distances—the distance between any two vertices in the subgraph is the same as the distance between those vertices in the hypercube. Equivalently, a partial cube is a graph whose vertices can be labeled with bit strings of equal length in such a way that the distance between two vertices in the graph is equal to the Hamming distance between their labels. Such a labeling is called a Hamming labeling; it represents an isometric embedding of the partial cube into a hypercube.