  Diamond graphs and Laakso graphs are important examples in the theory of
metric embeddings. Many results for these families of graphs are similar to
each other. In this connection, it is natural to ask whether one of these
families admits uniformly bilipschitz embeddings into the other. The well-known
fact that Laakso graphs are uniformly doubling but diamond graphs are not,
immediately implies that diamond graphs do not admit uniformly bilipschitz
embeddings into Laakso graphs. The main goal of this paper is to prove that
Laakso graphs do not admit uniformly bilipschitz embeddings into diamond
graphs.
