  Let $\mathcal{E}$ be a $\mathbb{Q}$-isogeny class of elliptic curves defined
over $\mathbb{Q}$. The isogeny graph associated to $\mathcal{E}$ is a graph
which has a vertex for each elliptic curve in the $\mathbb{Q}$-isogeny class
$\mathcal{E}$, and an edge for each cyclic $\mathbb{Q}$-isogeny of prime degree
between elliptic curves in the isogeny class, with the degree recorded as a
label of the edge. In this paper, we define an isogeny-torsion graph to be an
isogeny graph where, in addition, we label each vertex with the abstract group
structure of the torsion subgroup over $\mathbb{Q}$ of the corresponding
elliptic curve. Then, the main result of the article is a classification of all
the possible isogeny-torsion graphs that occur for $\mathbb{Q}$-isogeny classes
of elliptic curves defined over the rationals.
