A Good Drawing of Complete Bipartite Graph K9,9, Whose Crossing Number Holds Zarankiewicz Conjectures

There exist some Drawing for any graph G = (V,E) on plan. An important aim in Graph Theory and Computer science is obtained a best drawing of an arbitrary graph. Also, a draw of a non-planar graph G on plan generate several edge-cross. A good drawing (or strongly best drawing) of G is consist of minimum edge-cross. The crossing number of a graph G, is the minimum number of crossings in a drawing of G in the plane, denoted by cr(G). A crossing is a point of intersection between two edges. The crossing number of the complete bipartite graph is one of the oldest crossing number open problems. In this paper, we present a good drawing of complete bipartite graph K9,9. This drawing is able to developed on Kn,n, ∀n ≤ 9 and implies that the crossing number of these graphs hold Zarankiewicz conjecture. ∀n,m ∈ N Zarankiewicz conjecture is equal to cr(Kn,m) ? =Z(m,n) = [ m 2 ][ m− 1 2 ][ n 2 ][ n− 1 2 ].