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In this paper, we research the grid homology for spatial graphs with cutedges. We show that the grid homology for spatial graph $f$ is trivial if $f$has sinks, sources, or cut edges. As an application, we give a purelycombinatorial proof of a K\"{u}nneth formula for the knot Floer homology ofconnected sums in the framework of the grid homology.

Grid homology for spatial graphs and a K\"{u}nneth formula of connected sum