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

M. MALATHI*, N. SELVI, J. RAVI SANKAR

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.


Keywords


Crossing number, edge crossing number, Zero Divisor Graph, Rectilinear crossing number.

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