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Abstract

Let R be a commutative ring and let Z(R) be its set of zero-divisors. We associate a graph (R) to R with vertices Z(R) * = Z(R)-{0}, the set of non-zero zero divisors of R and for distinct u, v Z(R) * , the vertices u and v are adjacent if and only if uv = 0. In this paper, we evaluate the consistency of rectilinear crossing number of complete bipartite zero divisor graphs, in which the transformation of a non-planar graph into a planar graph is obtained by framing formula using removal of edges and removal of crossings.