At first I must say I am from Mathematics background and I have a very little knowledge about programming in Python. I am working on drawing

The graph has

If you really need turtle graphics, it should be pretty straightforward to replace the string construction in this program with turtle moves.

CodePudding user response：

As http://garden.irmacs.sfu.ca/op/the_crossing_number_of_the_complete_bipartite_graph says, it is believed that the diagram you provided is always optimal. Put the one set on a vertical axis and the other on the horizontal, split close to evenly top/bottom, left/right. Then connect by straight lines. It is highly unlikely that you will find better than that.

You can see https://mathworld.wolfram.com/ZarankiewiczsConjecture.html for more, including various small n cases where it has been confirmed.