Total graph of a module with respect to singular submodule

Let RR be a commutative ring with unity and MM be an RR-module. We introduce the total graph of a module MM with respect to singular submodule Z(M)Z(M) of MM as an undirected graph T(Γ(M))T(Γ(M)) with vertex set as MM and any two distinct vertices xx and yy are adjacent if and only if x+y∈Z(M)x+y∈Z(M). We investigate some properties of the total graph T(Γ(M))T(Γ(M)) and its induced subgraphs Z(Γ(M))Z(Γ(M)) and Z¯(Γ(M)). In some aspects, we have noticed some sort of finiteness.