关于<c_4,n>∪<c_4,n>∪_(p_m)的优美性

On the Gracefulness of <c_4,n>∪<c_4,n>∪_(p_m)

图c4是4个顶点的圈,<c4,n>是将n个c4的对应顶点粘接到一起得到的图,pm=u0,u1…um是m+1个顶点的简单通路.图<c4,n>∪<c4,n>∪pm是两个<c4,n>与一个pm的不交并.本文得到了<c4,n>∪<c4n>∪pm(m,n≥1(m≠2))是优美的.

For i=1,2,…,n let vi,1,vi,2,vi,3vi,4 be a 4-cycle.c4,n be a graph as one obtained by identifying vi,1 for all i,Pm be a path with m＋1 vertices.The graph 〈c4,n〉∪〈c4,n〉∪pm denotes the disjoint union of two copies 〈C4,n〉 and Pm.In this pager,The graph 〈c4,n〉∪〈c4,n〉∪pm is proved to be graceful for all n and m（m≠2）.