Because the algorithm chooses C and P1 and then ignores P2N-1, for the Eperim doesn't the algorithm select every other vertex? I'm confused regarding how to determine the cover and approximation ratio given that Espoke will have only C and p1 as a cover because it vertex C covers all other edges.

Consider the wheel graph Wn which has vertex set V={c,p1,p2,,p2n1,p2n}, and edge set E=EperimEspoke where Eperim={(p1,p2),(p2,p3),,(p2n1,p2n),(p2n,p1)} and Espoke={(c,p1),(c,p3),,(c,p2n1)}. (a) For the Vertex Cover approximation algorithm presented in lecture, determine the resulting cover and approximation ratio when the algorithm is applied to Wn and the edges are presented to the algorithm as (c,p1),(c,p3),,(c,p2n1),(p1,p2),(p2,p3),,(p2n1,p2n). Explain vour reasoning