(Biplanar Crossing Number) A graph G drawn in the plane may contain edge crossings, namely intersections among pairs of edges that are not vertices. One constraint in crossing number problems is that no three edges may intersect in a single point (with the exception of vertices). The crossing number of a graph G, written (G), is the fewest possible number of (non-vertex) edge crossings over all drawings of G. For example if G is planar then (G) = 0. And (K5) = 1 (verify this claim). The biplanar crossing number of a graph G is the smallest number of crossings of G over all drawings of G, where you are now allowed to use two (2) layers to draw the graph. In other words, replicate the set of vertices and distribute the edges among the two layers. The biplanar crossing number of a graph G is written 2(G). Problem. Determine 2(Kn) for n = 5; 6; 7; 8; 9; 10; 11; and 12. Prove that your answers are correct. Problem. You define the t-planar crossing number and investigate the above problem for many values of t. Note that 2-planar and biplanar mean the same thing.