Actually what I think they have meant to ask about the complete bipartite graph (It seems to be spelling mistake in the question)..
For that case , we have the relation between the independence number and chromatic number as :
Independence number >= Number of vertices / Chromatic number
Secondly chromatic number of a complete bipartite graph is 2.
Hence size of maximal independent set which is independence number >= (m+n) / 2 [ As the graph is Km,n so is the case here ]
= ceil[(m + n) / 2]
Hence D) should be the correct option.