Let 𝐾𝐾 be a field, 𝐸𝐸 is a directed graph. Let 𝐴𝐴~ is a directed line graph. Suppose that 𝑉𝑉[𝑝𝑝] is a class of Chen simple module for the Leavitt path algebra (𝐿𝐿𝐾𝐾 (𝐸𝐸)), with [p] being equivalent classes containing an infinite path. An infinite path p is an infinite sequence from the sides of a graph. In this paper it will be shown that 𝑉𝑉[𝑝𝑝]is not a prime module of the Leavitt path algebra for graph 𝐴𝐴∞ .Keywords : Leavitt path algebra, Graph 𝐴𝐴~, Chen simple modules, Prime modules

We characterize a graded simple module  in the setting Leavitt path algebras L which is the completely prime module. Let m  M  and r  A, an A-module M is called a completely prime module if    for one m  M  and r  A then 0  or m = 0. In this article, we show that If u is a sink or an infinite emitter, then a graded simple module which is simple  is not a completely prime module.