Co-maximal signed graphs of commutative rings.

Let Γ(R) be a graph with element of R (finite commutative ring with unity) as vertices, where two vertices a and b are adjacent if and only if Ra + Rb = R. In this paper, we characterize the rings for which a co-maximal meet signed graph ΓΣ(R), a co-maximal join signed graph Γ ∨ Σ (R), a co-maximal ring sum signed graph Γ ⊕ Σ (R), their negation signed graphs η(ΓΣ(R)), η(Γ ∨ Σ (R)), η(Γ ⊕ Σ (R)) respectively and their line signed graphs are balanced, clusterable, and sign-compatible. [ABSTRACT FROM AUTHOR]