ABSTRACT
In this chapter, we present one of the most important results about Cartesian products from the area of metric graph theory. It asserts that any graph has a canonical metric representation as an isometric subgraph of a Cartesian product. A graph embeds via the identity mapping into itself, in which case the representation is trivial. However, as soon as the representation gives an isometric embedding into the Cartesian product of more than one factor, the representation yields several useful properties of the embedded graph.
