LAUSR

For a commutative ring R with unity ( $$1\ne 0$$ 1 ≠ 0 ), the zero-divisor graph of R , denoted by $$\varGamma (R)$$ Γ ( R ) , is a simple graph with vertices as elements of R and two distinct vertices are adjacent whenever the product of the vertices is zero. Further, its signed zero-divisor graph is an ordered pair $$\varGamma _{\varSigma }(R):= (\varGamma (R), \sigma )$$ Γ Σ ( R ) : = ( Γ ( R ) , σ ) , where for an edge xy , $$\sigma (xy)$$ σ ( x y ) is ‘ $$+$$ + ’ if either x or y or both is a nonzero zero-divisor and ‘−’ otherwise. This article aims at gaining a deeper insight into signed zero-divisor graphs by investigating properties such as balancing, clusterability, sign-compatibility, consistency, $$\mathcal {C}$$ C -sign-compatibility, and $$\mathcal {C}$$ C -consistency.