齿轮图n是在轮n的轮圈cn上每相邻点之间都加入一个顶点后得到的图,pm是m+1个顶点的简单通路,图n∪n∪pm是两个n的拷贝与一个pm的不交并.证明了n≥3,m=1或m≥3,图n∪n∪pm是优美的.
A gear graph n is obtained from wheels wn=cn+k1 by adding a vertex between every pair of adjacent vertices of the cycle.In this paper,the graph n∪n∪pm is proved to be graceful for all n≥3 and m(m≠2).