Let G(V

E

F) be a planar graph

the complate chromatic number rc(G) G is the minimum num ber colours required for colouring the elements of V∪E∪F

so that the associate elements have differ ent colours(adjacent or incident). We have got as follows: xc(W1)=p(p≥6)

xc(F1)=p(p≥6)

xc(G0)≤△(G)+4

xc(Pl×m)=6(l

m≥2

l≡m≡0(mod2)). Where W1

F1 and G0 denots wheel graphs

fan graphs

outerplanar graphs and planar latticed graphs separately.