Abstract
We examine the class of distance regular graphs which can be embedded in a cube. We show that in the case of isometric embedding they are precisely the cubes, the even cycles and the ‘revolving doors’—a ‘revolving door’ is the subgraph of an odd dimensional cube whose vertices are as evenly balanced in the number of 1's and 0's as possible. In the general case we show that if the girth of the graph is 4, then it must be a cube, and we also obtain some bounds on the parameters of the graph.
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