• M.Malathi
• N.Selvi

Let R be a commutative ring and let Z(R) be its set of zero- divisors. We associate a graph Γ(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 survey some ways of transforming a non-planar graph into a planar for complete zero divisor graphs, and discuss measures to obtain the planarity of a graph. We also characterize both the minimum and maximum number of edge crossings possible in particular Zero divisor graph classes. First we define the maximum rectilinear crossing number (MRCN) of a graph G, denoted by CR(Γ(Z_n)) where we seek a straight line drawing maximizing the number of edge crossings and secondly we recall the minimum rectilinear crossing number of zero divisor graphs especially for complete graph. Ultimately we investigate, the Maximum planar sub graphs of these maximum and minimum Rectilinear crossing number of zero divisor graphs.

Rectilinear Crossing number, planar graph, Zero Divisor Graph

"CONSISTENCY OF MAXIMUM PLANARITY IN RECTILINEAR CROSSING NUMBER OF COMPLETE ZERO DIVISOR GRAPH", International Journal of Emerging Technologies and Innovative Research (www.jetir.org), ISSN:2349-5162, Vol.5, Issue 7, page no.763-768, July-2018, Available :http://www.jetir.org/papers/JETIR180Z006.pdf

"CONSISTENCY OF MAXIMUM PLANARITY IN RECTILINEAR CROSSING NUMBER OF COMPLETE ZERO DIVISOR GRAPH", International Journal of Emerging Technologies and Innovative Research (www.jetir.org | UGC and issn Approved), ISSN:2349-5162, Vol.5, Issue 7, page no. pp763-768, July-2018, Available at : http://www.jetir.org/papers/JETIR180Z006.pdf