C <sub> 2j +1 </ Sub> Uc <sub> 2k </ Sub> Class To Reconcile The Figure,

We write n V(G), qE(G). AfinitegraphG=(V(G), E(G)) is said to be harmonious if there is an injection f: V(G)Z, Zq is the integer group modulo q, such that the induced function f*: E(G) Z defined by f* (xy)≡(f(x)+f(y)) (mod q), x, y∈V(G) is a bijection. Let C be the cycle with n vertexes0 In this paper, it proved that the disjoint union of cycles C2~+1 UC2(j≥1,k≥2 and (j,k)≠(1,2)) is a harmonious graph. Up to this, we give a conjecture that the disjoint union of m cycles C UC U UC isaharmoniousgraphifandonlyif Zrz is odd and k(m),where k(m) is an integer big enough.