Abstract
The sum-essential graph [Formula: see text] of a left [Formula: see text]-module [Formula: see text] is a graph whose vertices are all nontrivial submodules of [Formula: see text] and two distinct submodules are adjacent if and only if their sum is an essential submodule of [Formula: see text]. Properties of the graph [Formula: see text] and its subgraph [Formula: see text] induced by vertices which are not essential as submodules of [Formula: see text] are investigated. The interplay between module properties of [Formula: see text] and properties of those graphs is studied.
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