关于图C_m∪P_(n-1)^+的优美性

The Graceful Labels of the Graphs C_m∪P_(n-1)^+

图Ｃｍ ∪Ｐ＋ｎ－ １ 是圈Ｃｍ 与Ｐ＋ｎ－ １ 的不交并。本文证明了当①ｍ ＝ ４ｋ，ｎ ≥ｋ ＋ ２；②ｍ ＝ ４ｋ ＋ １，４ｋ － １ ≤ｎ ≤１０ｋ－ ７；③ｍ ＝ ４ｋ＋ ２，ｎ ≥４ｋ ＋ １；④ｍ ＝ ４ｋ ＋ ３，４ｋ＋ ２≤ｎ ≤１０ｋ－ ２ 时，图Ｃｍ ∪Ｐ＋ｎ－ １ 是优美的。

Let G=(V,E) be a simple graph and f:V→{0,1,…,|E|} be an injection.Define an induced map f:E→{1,2,…,|E|} by f (uv)=|f(u)-f(v)| for vu∈E. If fis a bijection,f is said to be a graceful labeling of G,and the graph G is said to be graceful.The graph C m ∪ P + n-1 is the disjoint union of cycle C m and P + n-1 .In this paper,we proved the graphs C m ∪ P + n-1 are graceful,when n≥k+2,m=4k;n≥4k+1,m=4k+2;4k-1≤n≤10k-7,m=4k+1;4k+2≤n≤10k-2,m=4k+3.