Suppose that G is isomorphic with its compliment (I cant put the bar on top of G so let G compliment be denoted by Gand that n=|V(G)|=4*k+1for some integer k>=1 (G is the complement of G). Suppose that the degree sequence of G is d_1>=d_2>=...>=d_n.
a) Prove that d_i+d_(n-i+1)=n-1 for each i=1,2,...n.
b) Use (a) to prove G has at least one vertex with degree (n-1)/2.
NOTE: this _ is meant to indicate a subscript hence d_(n-i+1) means the entire (n-i+1) is a subscript of d.
I am very stuck on how I got about proving part a and as a consequence part B. I can draw what happens and think I understand the premise BUT the prooof has me kuffafeld .
Help would be utterly and forever appreciated.
THANK YOU!