Excited about Math

So, for the past 4 weeks, I have understood about 3% of what I have been doing. I finally have something I am excited about and can actually do. I am now trying to construct a graph with 457 vertices that has no triangles, rectangles, ... ,hexagons, in it. I actually have a plan of attack for it and everything. And, to my knowledge, nobody has discovered this graph. Hooray for math!