For every d at least 2, the full Kontsevich graph complex maps injectively into the Chevalley-Eilenberg complex of the n=d-1 Schouten algebra, so its zeroth cohomology acts via L-infinity automorphisms on graded symplectic manifolds.
Differentials on graph complexes
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abstract
We study the cohomology of complexes of ordinary (non-decorated) graphs, introduced by M. Kontsevich. We construct spectral sequences converging to zero whose first page contains the graph cohomology. In particular, these series may be used to show the existence of an infinite series of previously unknown and provably non-trivial cohomology classes, and put constraints on the structure of the graph cohomology as a whole.
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M. Kontsevich's graph complexes and universal structures on graded symplectic manifolds
For every d at least 2, the full Kontsevich graph complex maps injectively into the Chevalley-Eilenberg complex of the n=d-1 Schouten algebra, so its zeroth cohomology acts via L-infinity automorphisms on graded symplectic manifolds.