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Let $Q_n$ be a hypercube graph and $\phi: Q_n\to G$ a surjective simplicial graph morphism i.e. if $u,v$ are adjacent vertices in $G$ then either $\phi(u)=\phi(v)$ or $\phi(u),\phi(v)$ are adjacent. Is there any intrinsic characterization of graphs $G$ which can be the image of such a map?

Let $Q_n$ be a hypercube graph and $\phi: Q_n\to G$ a surjective simplicial graph morphism i.e. if $u,v$ are adjacent vertices in $Q_n$ then either $\phi(u)=\phi(v)$ or $\phi(u),\phi(v)$ are adjacent. Is there any intrinsic characterization of graphs $G$ which can be the image of such a map?

Let $Q_n$ be a hypercube graph and $\phi: Q_n\to G$ a simplicial graph morphism i.e. if $u,v$ are adjacent vertices in $G$ then either $\phi(u)=\phi(v)$ or $\phi(u),\phi(v)$ are adjacent. Is there any intrinsic characterization of graphs $G$ which can be the image of such a map?

Let $Q_n$ be a hypercube graph and $\phi: Q_n\to G$ a surjective simplicial graph morphism i.e. if $u,v$ are adjacent vertices in $G$ then either $\phi(u)=\phi(v)$ or $\phi(u),\phi(v)$ are adjacent. Is there any intrinsic characterization of graphs $G$ which can be the image of such a map?