(A) χ(G) ≥ a(G) ,counter ex :Cycle graph with n vertices(n is even) has χ(G) = 2 and a(G) = n/2 .Hence (A) is False.
(B)χ(G)≤a(G) ,counter ex :Complete graph with n vertices has χ(G) = n and a(G) = 1 .Hence (B) is False.
(C)a(G)≥n/χ(G), is always True.
Theorem: The vertices of G can be partitioned into χ(G) monochromatic classes. Each class is an independent set, and hence cannot have size larger than α(G),
α(G) χ(G) ≥ n or
a(G)≥n/χ(G) .
The correct answer is (C)a(G)≥n/χ(G)