  Erd\H{o}s, Harary, and Tutte defined the dimension of a graph $G$ as the
smallest natural number $n$ such that $G$ can be embedded in $\mathbb{R}^n$
with each edge a straight line segment of length 1.
  Since the proposal of this definition, little has been published on how to
compute the exact dimension of graphs and almost nothing has been published on
graphs that are minor minimal with respect to dimension. This paper develops
both of these areas. In particular, it (1) establishes certain conditions under
which computing the dimension of graph sums is easy and (2) constructs three
infinitely-large classes of graphs that are minor minimal with respect to their
dimension.
