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Let R(+)N be the idealization of the ring R by the R-module N. In this paper, we investigate when Γ(R(+)N) is a Planar graph where R is an integral domain and we investigate when Γ(Zn(+)Zm) is a Planar graph.

In this paper, we have constructed a sequence of soft points in one soft set with respect to a fixed soft point of another soft set. The convergence and boundedness of these sequences in soft ∆-metric spaces are defined and their properties are established. Further, the complete soft ∆-metric spaces are introduced by defining soft ∆-Cauchy sequences.

Let R be a commutative principal ideal ring with unity. In this paper, we classify when the intersectiongraphs of ideals of a ring R G(R), is a divisor graph. We prove that the intersection graphs of ideals of a ring RG(R), is a divisor graph if and only if R is a local ring or it is a product of two local rings with each of them hasone chain of ideals. We also prove that G(R), is a divisor graph if it is a product of two local rings one of themhas at most two non-trivial ideals with empty intersection.