Line Signed Graph of a Signed Total Graph

A signed total graph is an ordered pair TΣ(Γ(R)):=(T(Γ(R)),σ), where T(Γ(R)) is the total graph of a commutative ring R, called the underlying graph of TΣ(Γ(R)) and TΣ(Γ(R)) is associated with a signing of its edges (a, b) by the function σ such that σ(a,b) is '+' if a∈Z(R) or b∈Z(R) and '−' otherwise. The aim of this paper is to gain a deeper insight into the notion of signed total graph by characterizing the rings for which line signed graph L(TΣ(Γ(R))) of signed total graph are C-consistent, TΣ(Γ(R))-consistent and sign-compatible.