Abstract: Diab proved the following graphs are Cordial; P_mK_1,n if and only if (m,n) =(1,2); C_mK_1,n; P_mK_n; C_mK_n for all m and n except m≡2(mod 4). In this paper, we proved the Cordiality on the union of 3-regular connected graph K₃ and cycle C_m. First we have the Lemma 2, if uv∈ E(G), G is Cordial, we add 4 vertices x, y, z, w in sequence to the edge uv, obtain a new graph denoted by G*, then G* is still Cordial, by this lemma, we consider four cases on the union of 3-regular connected graph R₃, and for every case we distinguish four subcases on the cycle C_m. 

Key words: 3-regular graph, Cordial graph, union graph