If d_{max} is the maximum degree of a vertex in a graph then the chromatic number of G
k(G) $\leq$ d_{max} +1
This upper bound can be improved by 1 if the graph G has no complete graph of d_{max}_{ }+1 vertices
so in this case K(G)$\leq$d_{max}
Since, in this graph d_{max}=4, atmost 4 colors are needed to color this graph so first eliminate option (d).