Total graph of a module with respect to singular submodule

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