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Assume that U is a left R-semimodule, R is an abelian semiring with nonzero identity. The co-intersection graphs of U, indicated by Γ (U), an undirected graph whose nods set is the collection of all non-trivial subsemimodules of U with two distinct nods X, Y are adjacent if and only if X+ Y≠ U. These graphs was studies to relate the combinatorial possessions of Γ (U) to the algebraic possessions of the R-semimodule U. Connectedness and planarity were for Γ (U). Also, studies are done on the girth, diameter, clique and chromatic number of this graphs.