A digraph D(V, E) is said to be graceful if there exists an injection f : V(G) →{0, 1,... , |E|} such that the induced function f' : E(G) --~ {1, 2,… , |E|} which is defined by f' (u, v) = [f(v) - ...A digraph D(V, E) is said to be graceful if there exists an injection f : V(G) →{0, 1,... , |E|} such that the induced function f' : E(G) --~ {1, 2,… , |E|} which is defined by f' (u, v) = [f(v) - f(u)] (rood |E|+ 1) for every directed edge (u, v) is a bijection. Here, f is called a graceful labeling (graceful numbering) of D(V, E), while f' is called the induced edge's graceful labeling of D. In this paper we discuss the gracefulness of the digraph n- Cm and prove that n. Cm is a graceful digraph for m = 15, 17 and even展开更多
文摘A digraph D(V, E) is said to be graceful if there exists an injection f : V(G) →{0, 1,... , |E|} such that the induced function f' : E(G) --~ {1, 2,… , |E|} which is defined by f' (u, v) = [f(v) - f(u)] (rood |E|+ 1) for every directed edge (u, v) is a bijection. Here, f is called a graceful labeling (graceful numbering) of D(V, E), while f' is called the induced edge's graceful labeling of D. In this paper we discuss the gracefulness of the digraph n- Cm and prove that n. Cm is a graceful digraph for m = 15, 17 and even