A digraph D(V, E) is said to be graceful if there exists an injec-tion f : V(D) { 0, 1, ... , |E|} such that the induced func-tion f': E(D) 4 { 1, 2, ... , |E|} which is defined by f' ('u, v) = [f(v) - f(u)] (mod (|E| 1)) for every directed edge (u, v) is a bi-jection. Here, f is called a graceful labeling(graceful numbering) of digraph D(V, E), while f' is called the induced edge's graceful label-ing of digraph D(V, E). In this paper, we discuss the gracefulness of the digraph n - C_m and prove the digraph n - C_(15) is graceful for even n.
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机译：如果存在射入f，则有向图D（V，E）被认为是优美的：V（D）{0，1，...，| E |}使得诱导函数f'：E （D）4 {1，2，...，| E |}由f'（'u，v）= [f（v）-f（u）]（mod（| E | 1））定义对于每个有向边（u，v）都是双射。在这里，f被称为有向图D（V，E）的优美标注（优美编号），而f'被称为有向图D（V，E）的诱导边缘优美的标示。在本文中，我们讨论了有向图n-C_m的优美性，并证明了有向图n-C_（15）对于n也很优美。
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