Consider two graphs $G_1 = (V_1, E_1)$ and $G_2 = (V_2, E_2)$. How to define a mapping function $f: V_1 \rightarrow V_2$ that preserves the adjacency in both graphs?
EDIT: Thanks for answering! $G_1$ and $G_2$ are not necessarily isomorphic but $V_2(G_2) \subseteq V_1(G_1)$, hence function f is non-injective and surjective. Function f should be an adjacency preserving epimorphism from $G_1$ to $G_2$.
If the question is asking for a bijective homomorphism (adjacency preserving) map $f$ between the two, then $f$ isn't guaranteed unless $G_1$ and $G_2$ are isomorphic, by definition. However if you just want a homomorphism $f$ from $V_1$ to $V_2$, then you could have $f$ be the trivial map that sends all the vertices of $V_1$ to a single vertex in $V_2$ with a loop (if one exists). If no such vertex in $V_2$ exists, then it isn't clear that there is even a trivial homomorphism between $V_1$ and $V_2$. For example, let $V_2$ the graph of a single point without a loop. Then any map from $V_1$ to $V_2$ won't be a homomorphism unless $V_1\cong V_2$ (isomorphic) or $V_2$ is a larger collection of unadjacent points.