Reza Beyranvand - Department of Mathematics, Lorestan university, Khoramabad, Iran.
Parvin Karimi Beiranvand - Department of Mathematics, Islamic Azad University, Khorramabad branch, Khoramabad, Iran.

Let M be a module over a commutative ring R. We continue our study of strongly annihilating submodule graph SAG(M) introduced in [۹]. In addition to providing the more properties of this graph, we introduce the subgraph SAG∗(M) of SAG(M) and compare the properties of SAG∗(M) with SAG(M) and AG(M) (the annihilating submodule graphof M introduced in [۵])

Aannihilating submodule graph, coloring number, star graph, strongly annihilating submodule graph