For each vertex x, let C(x) ={z:x~z}. Prove the following:

i) For all vertices x and y, either C(x)=C9Y) or else . In other words two of the sets C(x) and C(y) cannot intersect unless they are equal.

ii) if , then there does not exist an edge joining a vertex in C(x) to a vertex in C(y)