Reza Beyranvand - Department of Mathematics, Lorestan university, Khorramabad, Iran
Ahadollah Farzi-Safarabadi - Department of Mathematics, Lorestan University, Khorramabad, Iran

In this paper, we define the notion of strongly annihilating-submodule graph of modules. This graph is a straightforward common generalization of the annihilating-submodule graph  and the annihilating-ideal graph. In addition to providing the properties of this graph in general, we investigate the behavior of the graph when modules are reduced or divisible.

Annihilating-submodule graph, Strongly annihilating-submodule graph, reduced module, divisible module