  Let $\mathcal{E}$ be a $\mathbb{Q}$-isogeny class of elliptic curves defined
over $\mathbb{Q}$ without CM. The isogeny graph associated to $\mathcal{E}$ is
a graph which has a vertex for each elliptic curve in $\mathcal{E}$ and an edge
for each $\mathbb{Q}$-isogeny of prime degree that maps one elliptic curve in
$\mathcal{E}$ to another elliptic curve in $\mathcal{E}$, with the degree
recorded as a label of the edge. An isogeny-torsion graph is 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 statement of the article is a classification of the $2$-adic
image of Galois that occurs at each vertex of all isogeny-torsion graphs
consisting of elliptic curves defined over $\mathbb{Q}$ without CM.
