The sum-essential graph $ \mathcal{ S}_R(M) $ of a left $R$-module $M$ is a graph whose vertices are all nontrivial submodules of $M$ and two distinct submodules are adjacent iff their sum is an essential submodule of $M$. Properties of the graph $\mathcal{ S}_R(M)$ and its subgraph $\mathcal{ P}_R(M)$ induced by vertices which are not essential as submodules of $M$ are investigated. The interplay between module properties of $M$ and properties of those graphs is studied.
Categories: math.RA math.CO