Total graph of a module with respect to singular submodule - Jituparna Goswami; Kukil Kalpa Rajkhowa; Helen K. Saikia (Arab Journal of Mathematical Sciences, 2016)
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.