非连通图C_(12)(r_1,0,r_2,0,···,r_6,0)UF_(k,4)的优美标号

THE GRACEFUL LABELING OF THE UNCONNECTED GRAPH C_(12)(r_1,0,r_2,0,···,r_6,0)UF_(k,4)

讨论了非连通图C12(r1,0,r2,0,…,r6,0)∪F k,4的优美性,证明了a,k,r i(i=1,2,…,6),为任意自然数,且当r5=r6=0,k=3,r6=a,r5≥2-a,k=4;r6≥4,k=5时,非连通图C12(r1,0,r2,0,…,r6,0)∪F k,4是交错图。其中C12(r1,0,r2,0,…,r6,0)∪F k,4表示圈C12的(r1,0,r2,0,…,r6,0)-冠,把顺序有一个公共点的k个C4的连通并图记作F k,4。

The gracefulness of the unconnected graph C12（r1,0,r2,0,…,r6,0）∪Fk,4 is discussed. Furthermore, we prove the following results：For any natural number a,k,ri（i=1,2,…,6）,if r5=r6=0,k=3,r6=a,r5≥2-a,k=4;r6≥4,k=5, then the unconnected graphs C12（r1,0,r2,0,…,r6,0）∪Fk,4 are balanced bipartite graph.