ABSTRACT
The main theme of this chapter is the canonical isometric embedding, which embeds any graph isometrically into a Cartesian product. We begin by defining the map, proving that it is an isometry, and deducing several of its properties. Then we take a closer look at the role of the relation Θ in Cartesian products. Among others things, we prove that the only isometric irredundant embeddings into Cartesian products of complete graphs are the canonical isometric embeddings. We close with a description of the automorphisms of canonically embedded graphs.
