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For given closed orientable 3-manifolds $M$ and $N$ let $\c{D}(M,N)$ be theset of mapping degrees from $M$ to $N$. We address the problem: For which $N$,$\c{D}(M,N)$ is finite for all $M$? The answer is known in Thurston's pictureof closed orientable irreducible 3-manifolds unless the target is a non-trivialgraph manifold. We prove that for each closed non-trivial graph manifold $N$,$\c{D}(M,N)$ is finite for all graph manifold $M$.  The proof uses a recently developed standard forms of maps between graphmanifolds and the estimation of the $\widetilde{\rm PSL}(2,{\R})$-volume forcertain class of graph manifolds.

Finiteness of mapping degrees and ${\rm PSL}(2,{\R})$-volume on graph manifolds