路与圈并的奇优美标号算法
An Algorithm for Odd Graceful Labeling of the Union of Paths and Cycles
摘要：
1991年，Gnanajothi [4]证明了n点n-1边的路图P_n是奇优美的，m点m边的圈图C_m是奇优美的当且仅当m是偶数，她证明了当m是奇数时，圈图C_m不是优美的。本文首先研究了m = 4，6，8，10时的图C_m $\cup$ P_m，然后证明了当m为偶数时，图C_ $\cup$ P_n是奇优美的.最后给出了顶点集V（C_m $\cup$ P_n）和边集E（C_m $\cup$ P_n）的顶点和边的标号算法。
英文摘要：
In 1991, Gnanajothi [4] proved that the path graph P_n with n vertex and n-1 edge is odd graceful, and the cycle graph C_m with m vertex and m edges is odd graceful if and only if m even, she proved the cycle graph is not graceful if m odd. In this paper, firstly, we studied the graph C_m $\cup$ P_m when m = 4, 6,8,10 and then we proved that the graph C_ $\cup$ P_n is odd graceful if m is even. Finally, we described an algorithm to label the vertices and the edges of the vertex set V(C_m $\cup$ P_n) and the edge set E(C_m $\cup$ P_n).
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