
Abstract A signed total graph is an ordered pair T Σ ( Γ ( R ) ) : = ( T ( Γ ( R ) ) , σ ) , where T ( Γ ( R ) ) is the total graph of a commutative ring R, called the underlying graph of T Σ ( Γ ( R ) ) and T Σ ( 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 ( T Σ ( Γ ( R ) ) ) of signed total graph are C-consistent, T Σ ( Γ ( R ) ) -consistent and sign-compatible.
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