This question can also be solved using Pigeon-Hole Principle.
[ Following, Set is nothing but independant set( consisting of all colors of same type ). ]
1.Let the no. of Holes be represented by no. of independant sets( colors of same type ) and no. of Pigeons be represented be represented by no. of Vertices.
2.Here we are trying to distribute n Vertices(pigeons) into ϰ independant sets(holes).
3.As the n > ϰ ∴ there exists atleast one independant set(hole) which has ≽ n/ϰ Vertices(pigeons).
4.All the Vertices within the set are independant(are of same color) so they don’t have any edge between them, so they produce an independant set.
∴by Pigeon-Hole principle we can say that there exist an independant set having ≽ n/ϰ vertices.
Hence, a(G) ≥ n/ϰ(G).
Option (C) is correct.