• EDGE NON-EDGE CROSSING NUMBER OF BIPARTITE GRAPH OF Γ(Z_n )

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 [1,2]. In this paper we introduce the edge non-edge crossing number of bipartite zero divisor graphs. We evaluate for any non-outer planar graph, the minimum number of crossings between an edge and a non-edge whose edges are simple arcs, by framing definition for the drawing D of ENE crossing number.