Isometric Embeddings of Graphs into Hypercubes
We study in this chapter the graphs that can be isometrically embedded into hypercubes. We give several equivalent characterizations for these graphs in Theorems 19.1.1, 19.2.1, 19.2.5 and 19.2.8. As an application, one can recognize in polynomial time whether a graph can be isometrically embedded in a hypercube. Hypercube embeddable graphs admit, in fact, an essentially unique embedding in a hypercube; two formulations for the dimension of this hypercube are given in Propositions 19.1.2 and 19.2.12.
KeywordsShort Path Polynomial Time Distanee Matrix Positive Eigenvalue Isometric Embedding
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